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  • 1.
    Kopezhanova, Aigerim
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. LN Gumilyov Eurasian Natl Univ, Fac Mech & Math, Astana, Kazakhstan.
    Nursultanov, Erlan
    RUDN Univ, Moscow, Russia. Lomonosov Moscow State Univ, Kazakhstan Branch, Astana, Kazakhstan.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Artic Univ Norway, UiT, Narvik, Norway.
    A new generalization of Boas theorem for some Lorentz spaces lambda(q)(omega)2018Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, nr 3, s. 619-633Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let Lambda(q)(omega), q > 0, denote the Lorentz space equipped with the (quasi) norm parallel to f parallel to(Lambda q(omega)) := (integral(1)(0) (f*(t)omega(t))(q)dt/t)(1/q) for a function integral on [0,1] and with omega positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system Phi = {phi(k)}(k=1)(infinity) and generalized Lorentz Lambda(q) (omega) spaces.

  • 2.
    Blahota, I.
    et al.
    Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.
    Nagy, K.
    Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT the Arctic University of Norway, Narvik, Norway.
    Tephnadze, G.
    School of IT, Engineering and Mathematics, IV, University of Georgia, Tbilisi, Georgia.
    A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces2018Ingår i: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H-{p}} to the Lebesgue space L p {L-{p}} for all 0 < p ≤ 1 {0<p\leq 1}. We also prove that the result is sharp in a particular sense. 

  • 3.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convex Functions and Their Applications: A Contemporary Approach2018Bok (Refereegranskat)
    Abstract [en]

    This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics.  The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples.  Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.

    This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.

  • 4.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convex Functions on a Normed Linear Space2018Ingår i: Duality and Convex Optimization, Cham: Springer, 2018, s. 107-184Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Convex functions and their relatives are ubiquitous in a large variety of applications such as optimization theory, mass transportation, mathematical economics, and geometric inequalities related to isoperimetric problems. This chapter is devoted to a succinct presentation of their theory in the context of real normed linear spaces, but most of the illustrations will refer to the Euclidean space RN,">RN,RN, the matrix space MN(R)">MN(R)MN(R) of all N&#x00D7;N">N×NN×N-dimensional real matrices (endowed with the Hilbert–Schmidt norm or with the operator norm), and the Lebesgue spaces Lp(RN)">Lp(RN)Lp(RN) with p&#x2208;[1,&#x221E;]">p∈[1,∞]p∈[1,∞].

  • 5.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convex Functions on Intervals2018Ingår i: Duality and Convex Optimization, Cham: Springer, 2018, s. 1-70Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The study of convex functions of one real variable offers an excellent glimpse of the beauty and fascination of advanced mathematics. The reader will find here a large variety of results based on simple and intuitive arguments that have remarkable applications. At the same time they provide the starting point of deep generalizations in the setting of several variables, that will be discussed in the next chapters.

  • 6.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convex Sets in Real Linear Spaces2018Ingår i: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, s. 71-106Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The natural domain for a convex function is a convex set. In this chapter we review some basic facts, necessary for a deep understanding of the concept of convexity in real linear spaces. For reader’s convenience, all results concerning the separation of convex sets in Banach spaces are stated in Section 2.2 with proofs covering only the particular (but important) case of Euclidean spaces. Full details in the general case are to be found in Appendix  B

  • 7.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convexity and Majorization2018Ingår i: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, s. 185-226Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    This chapter is aimed to offer a glimpse on the majorization theory and the beautiful inequalities associated to it. Introduced by G. H. Hardy, J. E. Littlewood, and G. Pólya (Messenger Math. 58:145–152, (1929), [208]) in 1929, and popularized by their celebrated book on Inequalities (Hardy et al., Inequalities, Cambridge University Press, 1952, [209]), the relation of majorization has attracted along the time a big deal of attention not only from the mathematicians, but also from people working in various other fields such as statistics, economics, physics, signal processing, data mining, etc. Part of this research activity is summarized in the 900 pages of the recent book by A. W. Marshall, I. Olkin, and B. Arnold (Inequalities: theory of majorization and its applications. Springer, New York (2011), [305]).

  • 8.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convexity and Majorization2018Ingår i: Duality and Convex Optimization, Cham: Springer, 2018, s. 255-300Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems. The diet problem, the transportation problem, and the optimal assignment problem are among the many problems that during the Second World War and immediately after led L. Kantorovich, T. C. Koopmans, F. L. Hitchcock, and G. B. Danzig to develop the mathematical theory of linear programming. Soon it was realized that most results extend to the framework of convex functions, which marked the birth of convex programming. Later on, W. Fenchel, R. T. Rockafellar, and J. J. Moreau laid the foundations of convex analysis.

  • 9.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Convexity in Spaces of Matrices2018Ingår i: Duality and Convex Optimization, Cham: Springer, 2018, s. 227-254Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions F:Sym(n,R)&#x2192;R">F:Sym(n,R)→RF:Sym(n,R)→R whose values F(A) depend only on the spectrum of A. The main result concerns their description as superpositions f&#x2218;&#x039B;">f∘Λf∘Λ between convex functions f:Rn&#x2192;R">f:Rn→Rf:Rn→R invariant under permutations, and the eigenvalues map &#x039B;">ΛΛ.

  • 10.
    Abramovich, S.
    et al.
    Department of Mathematics, University of Haifa, Haifa, Israel.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UIT The Arctic University of Norway, Narvik, Norway.
    Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 3, s. 759-772Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

  • 11.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso, Norway. RUDN University, Moscow, Russia.
    Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, s. 201-215, artikel-id 21-16Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1

  • 12.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT The Artic University of Norway, Narvik, Norway.
    Oinarov, Ryskul
    L. N. Gumilyev Eurasian National University, Astana, Kazakhstan.
    Shaimardan, Serikbol
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. L. N. Gumilyev Eurasian National University, Astana, Kazakhstan.
    Hardy-type inequalities in fractional h-discrete calculus2018Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 73Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The first power weighted version of Hardy’s inequality can be rewritten as∫∞0(xα−1∫x01tαf(t)dt)pdx≤[pp−α−1]p∫∞0fp(x)dx,f≥0,p≥1,α<p−1,where the constant C=[pp−α−1]p is sharp. This inequality holds in the reversed direction when 0≤p<1. In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sharp.

  • 13.
    Burtseva, Evgeniya
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lundberg, Staffan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Arctic University of Norwa.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Multi–dimensional Hardy type inequalities in Hölder spaces2018Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, nr 3, s. 719-729Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

  • 14.
    Burtseva, Evgeniya
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Arctic University of Norway, Narvik, Norway.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Necessary and sufficient conditions for the boundedness of weighted Hardy operators in Hölder spaces2018Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, nr 11-12, s. 1655-1665Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study one‐ and multi‐dimensional weighted Hardy operators on functions with Hölder‐type behavior. As a main result, we obtain necessary and sufficient conditions on the power weight under which both the left and right hand sided Hardy operators map, roughly speaking, functions with the Hölder behavior only at the singular point to functions differentiable for and bounded after multiplication by a power weight. As a consequence, this implies necessary and sufficient conditions for the boundedness in Hölder spaces due to the corresponding imbeddings. In the multi‐dimensional case we provide, in fact, stronger Hardy inequalities via spherical means. We also separately consider the case of functions with Hölder‐type behavior at infinity (Hölder spaces on the compactified ).

  • 15.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces2018Ingår i: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 9, nr 1, s. 137-150Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient. 

  • 16.
    Høibakk, Ralph
    et al.
    UiT The Arctic University of Norway.
    Lukkassen, Dag
    UiT The Arctic University of Norway.
    Meidell, Annette
    UiT The Arctic University of Norway.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT The Arctic University of Norway.
    On some power means and their geometric constructions2018Ingår i: Mathematica Æterna, ISSN 1314-3336, E-ISSN 1314-3344, Vol. 8, nr 3, s. 139-158Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The main aim of this paper is to further develop the recently initiatedresearch concerning geometric construction of some power means wherethe variables are appearing as line segments. It will be demonstratedthat the arithmetic mean, the harmonic mean and the quadratic meancan be constructed for any number of variables and that all power meanswhere the number of variables are n = 2m, m 1 2 N for all powersk = 2􀀀q and k = 2q; q 2 N can be geometrically constructed.

  • 17.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. RUDN University, Moscow, Russia; UiT The Arctic University of Norway.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. School of Informatics, Engineering and Mathematics, The University of Georgia.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space H12018Ingår i: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 154, nr 2, s. 289-301Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove and discuss a new divergence result of Nörlund logarithmic means with respect to Vilenkin system in Hardy space H1.

  • 18.
    Niculescu, Constantin P.
    et al.
    Department of Mathematics, University of Craiova .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norway, Campus Narvik .
    Special Topics in Majorization Theory2018Ingår i: Duality and Convex Optimization, Cham: Springer, 2018, s. 301-326Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The primary aim of this chapter is to discuss the connection between the Hermite–Hadamard double inequality and Choquet’s theory. Noticed first by Niculescu (Math Inequal Appl 5(3):479–489, 2002, [356]), Niculescu (Math Inequal Appl 5(4):619–623, 2002, [357]) (during the conference Inequalities 2001, in Timişoara), this connection led him to a partial extension of the majorization theory beyond the classical case of probability measures, using the so-called Steffensen–Popoviciu measures. Their main feature is to offer a large framework under which the Jensen–Steffensen inequality remains available. As a consequence, one obtains the extension of the left-hand side of Hermite–Hadamard double inequality to a context involving signed Borel measures on arbitrary compact convex sets. A similar extension of the right-hand side of this inequality is known only in dimension 1, the higher dimensional case being still open.

  • 19.
    Blahota, I.
    et al.
    Institute of Mathematics and Computer Sciences, University of Nyìıregyhàza.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Two-sided Estimates of the Lebesgue Constants with respect to Vilenkin Systems and Applications2018Ingår i: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 60, nr 1, s. 17-34Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.

  • 20.
    Iqbal, Sajid
    et al.
    Department of Mathematics, University of Sargodha (Sub-Campus Mianwali), Mianwali, Pakistan.
    Pečarić, Josip
    Faculty of Textile Technology, University of Zagreb, Croatia.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UIT The Artic University of Norway.
    Tomovski, Zivorad
    aculty of Mathematics and Natural Sciences, Macedonia.
    Weighted Hardy-type inequalities involving convex function for fractional calculus operators2018Ingår i: Transactions of A. Razmadze Mathematical Institute, ISSN 2346-8092, Vol. 172, nr 2, s. 205-222Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to establish some new weighted Hardy-type inequalities involving convex and monotone convex functions using Hilfer fractional derivative and fractional integral operator with generalized Mittag-Leffler function in its kernel. We also discuss one dimensional cases of our related results. As a special case of our general results we obtain the results of Iqbal et al. (2017). Moreover, the refinement of Hardy-type inequalities for Hilfer fractional derivative is also included.

  • 21.
    Nikolova, Ludmila
    et al.
    Department of Mathematics and Informatics, Sofia University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norwa.
    Varošanec, Sanja
    Department of Mathematics, University of Zagreb.
    A new look at classical inequalities involving Banach lattice norms2017Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2017, artikel-id 302Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    ome classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of this type and also by deriving some new results related to classical Popoviciu’s, Bellman’s and Beckenbach-Dresher’s inequalities.

  • 22.
    Abylayeva, A.M.
    et al.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Baiarystanov, A.O.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, s. 683-694Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

  • 23.
    Abramovic, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Tromsø ; The Arctic University of Norway, Narvik.
    Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Ingår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, s. 599-609Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

  • 24.
    Kufner, Alois
    et al.
    Mathematical Institute, Czech Academy of Sciences, Department of Mathematics, University of West Bohemia.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Hardy type inequalities with kernels: The current status and some new results2017Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, nr 1, s. 57-65Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the general Hardy type operator inline image where inline image is a positive and measurable kernel. To characterize the weights u and v so that inline image is still an open problem for any parameters p and q. However, for special cases the solution is known for some parameters p and q. In this paper the current status of this problem is described and discussed mainly for the case inline image In particular, some new scales of characterizations in classical situations are described, some new proofs and results are given and open questions are raised.

  • 25.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Computer Science and Computational Engineering UiT,The Arctic University of Norway, Campus Narvik .
    Rafeiro, Humberto
    Ponticia Universidad Javeriana, Departamento de Matematicas Facultad de Ciencias.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Historical synopsis of the Taylor remainder2017Ingår i: Note di Matematica, ISSN 1123-2536, E-ISSN 1590-0932, Vol. 37, nr 1, s. 1-21Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we give an historical synopsis of various Taylor remainders and theirdierent proofs (without being exhaustive). We overview the formulas and the proofs given bysuch names as Bernoulli, Taylor, MacLaurin, Lagrange, Lacroix, Cauchy, Schlomilch, Roche,Cox, Turquan, Bourget, Koenig, Darboux, Amigues, Teixeira, Peano, Blumenthal, Wolfe andGoncalves. We end the paper with a new Taylor remainder which generalizes the well-knownLagrange remainder.

  • 26.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. The Arctic University of Norway.
    Rafeiro, Humberto
    Pontificia Universidad Javeriana, Bogotá, Colombia.
    On a Taylor remainder2017Ingår i: Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, ISSN 1786-0091, E-ISSN 1786-0091, Vol. 33, nr 2, s. 195-198Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note we derive a new Taylor remainder, which extends the well known Lagrange remainder as well as the obscure Goncalves remainder.

  • 27.
    Nikolova, Ludmila
    et al.
    Department of Mathematics and Informatics, Sofia University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Artic University of Norwa.
    Varošanec, Sanja
    Department of Mathematics, University of Zagreb.
    On continuous versions of some norm inequalities: ryska titeln: О НЕПРЕРЬIВНЬIХ ВАРИАНТОВ НЕКОТОРЬIХ НЕРАВЕНСТВ ДЛЯ НОРМ2017Ingår i: Proceedings Conference "Modern Problems of the analysis: Applications in Technique and Technology", Varonezh, Sept. 2017,  Actual directions of scientific research XXI century: Theory and Practice / [ed] M. Drapaljuk, Springer, 2017, s. 97-100Konferensbidrag (Refereegranskat)
    Abstract [ru]

    Представлено новое неравенство типа Бекенбах-Дрешера в терминах идеальных банаховых структур и неравенство типа Поповичу для бесконечного интерполяционного семейства

  • 28. Burtseva, Evgeniya
    et al.
    Lundberg, Staffan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Potential type operators in PDEs and their applications2017Ingår i: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, artikel-id 020178Artikel i tidskrift (Refereegranskat)
    Abstract [en]

     We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

  • 29.
    Oguntase, James Adedayo
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT The Arctic University of Norway, Narvik.
    Fabulerin, Olanrewaju Olanrewaju
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Adeagbo-Sheikh, Abdulaziz G.
    Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun.
    Refinements of some limit Hardy-type inequalities via superquadracity2017Ingår i: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 102, nr 116, s. 231-240Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Refinements of some limit Hardy-type inequalities are derived anddiscussed using the concept of superquadracity. We also proved that all threeconstants appearing in the refined inequalities obtained are sharp. The naturalturning point of our refined Hardy inequality is 𝑝 = 2 and for this case we haveeven equality.

  • 30.
    Kopezhanova, Aigerim
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Faculty of Mechanics and Mathematics L. N. Gumilyov, Eurasian National University.
    Nursultanov, Erlan
    Kazakhstan Branch of Lomonosov, Moscow State University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new two-sided inequalities concerning the Fourier transform2017Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 20, nr 3, s. 855-864Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).

  • 31.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The way to the top of science of professor R. Oinarov: Dedicated to the 70th birthday of Professor Ryskul Oinarov2017Ingår i: Eurasian Mathematical Journal, ISSN 2077-9879, Vol. 8, nr 2, s. 9-21Artikel i tidskrift (Refereegranskat)
  • 32.
    Kufner, Alois
    et al.
    Mathematical Institute, Czech Academy of Sciences.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Weighted inequalities of Hardy type2017 (uppl. 2)Bok (Övrigt vetenskapligt)
    Abstract [en]

    In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

  • 33.
    Memić, Nacima
    et al.
    Department of mathematics, University of Sarajevo.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients2016Ingår i: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 53, nr 4, s. 545-556Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

  • 34.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means2016Ingår i: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 13, nr 4, s. 1841-1853Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fejér means in this subspace is bounded from the Hardy space Hp to the space Lp for all 0 < p ≤ 1/2. Moreover, we prove that the result is in a sense sharp

  • 35.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
    Oinarov, Ryskul
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of a class of Hardy type operators2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 324Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.

  • 36.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces2016Ingår i: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, nr 2, s. 413-426Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces L p,φ (R n ,w), defined by a function φ(x,r) and radial type weight w(|x−x 0 |),x 0 ∈R n . These conditions are given in terms of inclusion into L p,φ (R n ,w), of a certain integral constructions defined by φ and w. In the case of φ=φ(r) we also provide easy to check sufficient conditions for that in terms of indices of φ and w.

  • 37.
    Nikolova, Ljudmila I.
    et al.
    Department of Mathematics, Kliment Ohridski University of Sofia, Department of Mathematics and Informatics, Sofia University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Varosanec, Sanja
    Department of Mathematics, University of Zagreb, University of Zagreb.
    Continuous Forms of Classical Inequalities2016Ingår i: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 13, nr 5, s. 3483-3497Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The main aim of this paper is to focus on the question to develop classical inequalities to hold in a more general “continuous” form (involving infinitely many functions and/or spaces). First, we discuss such developments concerning Hölder’s and Minkowski’s inequalities. After that we present such new general developments of Popoviciu’s and Bellman’s inequalities. Finally, we present some applications, possible extensions and questions for further research.

  • 38.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Inequalities for averages of quasiconvex and superquadratic functions2016Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

  • 39.
    Marcoci, Anca-Nicoleta
    et al.
    Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On a class of linear operators on lp and its Schur multipliers2016Ingår i: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 17, nr 2, s. 101-108Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider the spaces , , of infinite matrices defined by the norm . We consider the Schur product of matrices and prove that is not closed under this product. Moreover, we prove that linear and bounded operators on are Schur multipliers on , a result which is not obvious, since is not a Schur algebra. Most of the results are sharp in the sense that they are given via necessary and sufficient conditions. ( ) p w B 1p   A 1 ( ) =1 =1 1 0 := sup p p p jk k B j k w x p xk A a x            ( ) p w B p ( ) p w B ( ) p w B

  • 40.
    Oguntuase, James Adedayo
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Fabelurin, Olabiyi Olanrewaju
    Department of Mathematics, Obafemi Awolowo University. Ile-Ife, Osun State.
    Refinements of Hardy-type inequalities via superquadracity2016Ingår i: Publicationes mathematicae (Debrecen), ISSN 0033-3883, E-ISSN 2064-2849, Vol. 88, nr 3-4, s. 467-476Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Some new refinements of Hardy-type integral inequalities are derived, proved and discussed using the concept of superquadratic and subquadratic functions. The results obtained are generalizations and improvements of inequalities of this type in the literature.

  • 41.
    Baramidze, Lasha
    et al.
    Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Tephnadze, George
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 242Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove and discuss some new Hp-Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out

  • 42.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new estimates of the ‘Jensen gap’2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikel-id 39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

  • 43.
    Baǐarystanov, Askar O.
    et al.
    Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. The Artic University of Norway.
    Shaimardan, Serikbol
    Eurasian National University.
    Temirkhanova, Ainur
    Eurasian National University.
    Some new hardy-type inequalities in q-analysis2016Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 10, nr 3, s. 761-781Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q-analogs of (r, p)-weighted Hardy-type inequalities for all possible positive values of the parameters r and p. We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction

  • 44.
    Lukkassen, Dag
    et al.
    Narvik University College and Norut Narvik, UiT, The Arctic University of Norway, Narvik.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Stefan
    Universidade do Algarve, FCT, Campus de Gambelas, Universidade do Algarve, Faro.
    Some sharp inequalities for integral operators with homogeneous kernel2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikel-id 114Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    One goal of this paper is to show that a big number of inequalities for functions in L p (R + ) Lp(R+), p≥1 p≥1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0<p

  • 45.
    Lukkassen, Dag
    et al.
    Narvik University College and Norut Narvik.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Universidade do Algarve, FCT, Campus de Gambelas, Instituto Superior Tecnico, Research center CEAF.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some sharp inequalities for multidimensional integral operators with homogenous kernel: an overview and new results2016Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 551-564Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    One goal of this paper is to point out the fact that a big number of inequalities provedfrom time to time in journal publications, both one-dimensional and multi-dimensional, are particularcases of some general results for integral operators with homogeneous kernels, includingin particular, the statements on sharp constants.Some new multidimensional Hardy-Hilbert type inequalities are derived. Moreover, anew multidimensional P´olya-Knopp inequality is proved and some examples of applications arederived from this result. The constants in all inequalities are sharp.

  • 46.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, The Arctic University of Norway, Narvik, Norway.
    Shambilova, Guldarya E.
    Department of Mathematics, Financial University under the Government of the Russian Federation.
    Stepanov, Vladimir D.
    Department of Nonlinear Analysis and Optimization, Peoples’ Friendship University of Russia.
    Weighted Hardy type inequalities for supremum operators on the cones of monotone functions2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 237Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The complete characterization of the weighted Lp− Lr inequalities of supremum operators on the cones of monotone functions for all 0 < p, r≤ ∞ is given.

  • 47.
    Kalybay, Aigerim A.
    et al.
    Eurasian National University, Astana, Institute of Mathematics, Kazakhstan Ministry of Education and Sciences, KIMEP University, Abai Ave. 4, Almaty.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Temirkhanova, Ainur
    Faculty of Mathematics and Information Technologies, Eurasian National University, Munaitpasov st., 5, Astana.
    A New discrete Hardy-type inequality with kernels and monotone functions2015Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, artikel-id 321Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    new discrete Hardy-type inequality with kernels and monotone functions is proved for the case \(1< q< p<\infty\). This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out.

  • 48.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Universidade do Algarve, FCT, Campus de Gambelas, Instituto Superior Tecnico, Research center CEAF.
    A note on the best constants in some Hardy inequalities2015Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 9, nr 2, s. 437-447Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The sharp constants in Hardy type inequalities are known only in a few cases. In this paper we discuss some situations when such sharp constants are known, but also some new sharp constants are derived both in one-dimensional and multi-dimensional cases.

  • 49.
    Lukkassen, Dag
    et al.
    Narvik University College and Norut Narvik.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Hardy Type Operators in Local Vanishing Morrey Spaces on Fractal Sets2015Ingår i: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 18, nr 5, s. 1252-1276Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We obtain two-weighted estimates for the Hardy type operators fromlocal generalized Morrey spaces Lp,ϕloc (X,w1) defined on an arbitrary underlyingquasi-metric measure space (X, μ, ) with the growth condition, toLq,ψloc (X,w2), where w1 = w1[(x, x0)], x0 ∈ X is a weight of radial type,while w2 = w2(x) may be an arbitrary weight. The proof allows to simultaneouslytreat a similar boundedness V Lp,ϕloc (X,w1) → V Lq,ψloc (X,w2) forvanishing Morrey spaces. We obtain sufficient conditions for such estimatesin terms of some integral inequalities imposed on ϕ, ψ and w1.w2. We alsospecially treat the one weight case where w2(x) is also of radial type. Wedo not impose doubling condition on the measure μ, but base our result onthe growth condition.The obtained results show the explicit dependence of the mapping propertiesof the Hardy type operators on the fractional dimension of the set(X, μ, ). An application to spherical Hardy type operators is also given.

  • 50.
    Persson, Lars-Erik
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Narvik University College.
    Shambilova, Guldarya E.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow.
    Stepanov, Vladimir D
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University of Russia; Steklov Mathematical Institute, Russian Academy of Sciences.
    Hardy-type inequalities on the weighted cones of quasi-concave functions2015Ingår i: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 9, nr 2, s. 21-34Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The complete characterization of the Hardy-type Lp-Lq inequalities on the weighted cones of quasi-concave functions for all 0 < p, q < ∞ is given.

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