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  • 1.
    Abramovich, S.
    et al.
    Department of Mathematics, University of Haifa, Haifa, Israel.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UIT The Arctic University of Norway, Narvik, Norway.
    Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 3, p. 759-772Article in journal (Refereed)
    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] .

  • 2.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Inequalities for averages of quasiconvex and superquadratic functions2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 535-550Article in journal (Refereed)
    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.

  • 3.
    Abramovich, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new scales of refined Hardy type inequalities via functions related to superquadracity2013In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, no 3, p. 679-695Article in journal (Refereed)
    Abstract [en]

    For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

  • 4.
    Abramovich, Shoshana
    et al.
    University of Haifa, Department of Mathematics.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Pecaric, Josip
    University of Zagreb.
    Varosanec, Sanja
    University of Zagreb.
    General inequalities via isotonic subadditive functionals2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 1, p. 15-28Article in journal (Refereed)
    Abstract [en]

    In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

  • 5.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, no 2, p. 615-627Article in journal (Refereed)
    Abstract [en]

    In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

  • 6.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new scales of refined Jensen and Hardy type inequalities2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 3, p. 1105-1114Article in journal (Refereed)
    Abstract [en]

    Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

  • 7.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, Tromso, Norway. RUDN University, Moscow, Russia.
    Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 1, p. 201-215, article id 21-16Article in journal (Refereed)
    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

  • 8.
    Barza, Sorina
    et al.
    Luleå tekniska universitet.
    Burenkov, Victor
    School of Mathematics, University College Cardiff.
    Pecaric, Josip E.
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 53-67Article in journal (Refereed)
  • 9.
    Isac, George
    et al.
    Department of Mathematics and Computer Science, Royal Military College of Canada.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Inequalities related to isotonicity of projection and antiprojection operators1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 85-97Article in journal (Refereed)
    Abstract [en]

    The metric projection operator is an important tool in numerical analysis, optimization, variational inequalities and complementarity problems and has been considered from the point of view of isotonicity, with respect to an ordering compatible with the vector structure on Hilbert spaces and Banach spaces. In this paper, the authors study some inequalities related to the isotonicity of the metric projection operator onto a closed convex set in an ordered Banach space. The concept of antiprojection operator onto a compact nonempty subset of a Hilbert space is introduced and the relationship between the new inequality obtained by the authors and the isotonicity of such an operator is also discussed.

  • 10.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Lukkassen, Dag
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Svanstedt, Nils
    Chalmers University of Technology, Department of Mathematics.
    Imbeddings of anisotropic Orlicz-Sobolev spaces and applications2002In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 5, no 2, p. 181-195Article in journal (Refereed)
  • 11.
    Jain, Pankaj
    et al.
    University of Delhi, Department of Mathematics, Deshbandhu College.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Upreti, Priti
    University of Delhi, Motilal Nehru College, Department of Mathematics, New Delhi.
    On products of generalized Orlicz spaces2012In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 15, no 3, p. 663-674Article in journal (Refereed)
    Abstract [en]

    In the context of generalized Orlicz spaces, the products X-Phi 1 circle dot X-Phi 2 and X-Phi 1 circle times X-Phi 2 are studied and conditions are obtained under which these spaces are contained in a suitable space X-Phi. These imbedding results (inequalities) are in a sense sharp and for the case X = L-1, the conditions are even necessary and sufficient. Moreover, a new Holder type inequality is proved.

  • 12.
    Jain, Pankaj
    et al.
    Department of Mathematics, University of Delhi.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Carleman-Knopp type inequalities via Hardy inequalities2001In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 4, no 3, p. 343-355Article in journal (Refereed)
    Abstract [en]

    Some new Carleman-Knopp type inequalities are proved as "end point" inequalities of modern forms of Hardy's inequalities. Both finite and infinite intervals are considered and both the cases p q and q < p are investigated. The obtained results are compared with similar results in the literature and the sharpness of the constants is discussed for the power weight case. Moreover, some reversed Carleman-Knopp inequalities are derived and applied.

  • 13.
    Johansson, Maria
    et al.
    Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.
    Stepanov, Vladimir
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ushakova, Elena
    Hardy inequality with three measures on monotone functions2008In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 11, no 3, p. 393-413Article in journal (Refereed)
    Abstract [en]

    Characterization of Lvp[0, ∞) - L μq[O, ∞) boundedness of the general Hardy operator (Hsf)(x) =(∫[0,x] fsudλ) 1/s restricted to monotone functions f ≥ 0 for 0 < p.q.s < ∞ with positive Borel σ -finite measures λ, μ and v is obtained.

  • 14.
    Kaijser, Sten
    et al.
    Department of Mathematics, Uppsala University.
    Nikolova, Ludmila
    Department of Mathematics, Kliment Ohridski University of Sofia.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Hardy-type inequalities via convexity2005In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 8, no 3, p. 403-417Article in journal (Refereed)
    Abstract [en]

    A recently discovered Hardy-Pólya type inequality described by a convex function is considered and further developed both in weighted and unweighted cases. Also some corresponding multidimensional and reversed inequalities are pointed out. In particular, some new multidimensional Hardy and Pólya-Knopp type inequalities and some new integral inequalities with general integral operators (without additional restrictions on the kernel) are derived

  • 15.
    Kalybay, Aigerim
    et al.
    Eurasian National University, Astana.
    Oinarov, Ryskul
    Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Spectral properties of a class of singular differential operators2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 355-376Article in journal (Refereed)
  • 16.
    Kopezhanova, Aigerim
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Faculty of Mechanics and Mathematics L. N. Gumilyov, Eurasian National University.
    Nursultanov, Erlan
    Kazakhstan Branch of Lomonosov, Moscow State University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new two-sided inequalities concerning the Fourier transform2017In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 20, no 3, p. 855-864Article in journal (Refereed)
    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).

  • 17.
    Koroleva, Yulia
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On the weighted Hardy type inequality in a fixed domain for functions vanishing on the part of the boundary2011In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 14, no 3, p. 543-553Article in journal (Refereed)
    Abstract [en]

    We derive and discuss a new two-dimensional weightedHardy-type inequality in a rectangle for the class of functions fromthe Sobolev space $H^1$ vanishing on small alternating pieces of theboundary

  • 18.
    Krulic, Kristina
    et al.
    University of Zagreb.
    Pecaric, Josip
    University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new Hardy type inequalities with general kernels2009In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 12, no 3, p. 473-485Article in journal (Refereed)
    Abstract [en]

    We state and prove some new weighted Hardy type inequalities with an integral operator A(k) defined by A(k)f(x) := 1/K(x) integral(Omega 2) k(x,y)f(y)d mu(2) (y), where k : Omega(1) x Omega(2) --> R is a general nonnegative kernel, (Omega(1), mu(1)) and (Omega(2), mu(2)) are measure spaces and K(x) := integral(Omega 2) k(x,y)d mu(2) (y), x is an element of Omega(1). In particular, the obtained results unify and generalize most of the results of this type (including the classical ones by Hardy, Hilbert and Godunova).

  • 19.
    Lukkassen, Dag
    et al.
    Narvik University College and Norut Narvik.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Universidade do Algarve, FCT, Campus de Gambelas, Instituto Superior Tecnico, Research center CEAF.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some sharp inequalities for multidimensional integral operators with homogenous kernel: an overview and new results2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 551-564Article in journal (Refereed)
    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.

  • 20.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Equivalence of the Hölder-Rogers and Minkowski inequalities2001In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 4, no 2, p. 203-207Article in journal (Refereed)
    Abstract [en]

    It is well-known that the Hölder-Rogers inequality implies the Minkowski inequality. Infantozzi [6] observed implicitely and Royden [15] proved explicitely that the reverse implication is also true. In this note we discuss and give a new proof of this perhaps surprising fact

  • 21. Maligranda, Lech
    Why Hölder's inequality should be called Rogers' inequality1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 1, p. 69-83Article in journal (Refereed)
    Abstract [en]

    This reviewer remembers Leopold Fejér (1880-1959) saying (in Hungarian) that ``the history of mathematics serves to prove that nobody discovered anything: there was always somebody who had known it before'' (quoted in English in the present paper). The author argues convincingly about who had priority to the inequalities of Hölder (Rogers), Cauchy (Lagrange), Jensen (Hölder) and others. Also equivalences and relations between different forms and different inequalities and several proofs are offered. The paper concludes with biographical sketches of Leonard James Rogers and Otto Ludwig Hölder.

  • 22.
    Maligranda, Lech
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Nikolova, Ludmila
    Department of Mathematics, Sofia University.
    Persson, Lars-Erik
    Zachariades, T.
    Department of Mathematics, University of Athens, Panepistimiopolis.
    On n-th James and Khintchine constants of Banach spaces2008In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 11, no 1, p. 1-22Article in journal (Refereed)
    Abstract [en]

    For any Banach space X the n-th James constants J(n)(X) and the n-th Khintchine constants K-p,q(n)(X) are investigated and discussed. Some new properties of these constants are presented. The main result is an estimate of the n-th Khintchine constants K-p,q(n)(X) by the n-th James constants Jn (X). In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by Kato-Maligranda-Takahashi

  • 23.
    Maligranda, Lech
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Sabourova, Natalia
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Real and complex operator norms between quasi-banach Lp -L q spaces2011In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 14, no 2, p. 247-270Article in journal (Refereed)
    Abstract [en]

    Relations between the norms of an operator and its complexification as a mapping from Lp to Lq has been recognized as a serious problem in analysis after the publication of Marcel Riesz's work on convexity and bilinear forms in 1926. We summarize here what it is known about these relations in the case of normed Legesgue spaces and investigate the quasinormed case, i. e. we consider all 0 < p,q ≤ 8 . In particular, in the lower triangle, that is, for 0< p≤q≤∞ these norms are the same. In the upper triangle and the normed case, that is, when 1 ≤ q < p ≤ ∞ the norm of the complexification of a real operator is obviously not bigger than 2 times its real norm. In 1977 Krivine proved that the constant 2 can be replaced by √2 . On the other hand, it was suspected that in the case of quasi-normed Lebesgue spaces (0 < q < p ≤ ∞ ) the corresponding constant could be arbitrarily large, but as we will see this is not the case. More precisely, we prove that this constant for quasi-normed Lebesgue spaces is between 1 and 2. Some additional properties and estimates of this constant with some results about the relation between complex and real norms of operators, including those between two-dimensional Orlicz spaces are presented in the first four chapters. Finally, in Chapter 5, we use the results on the estimates of the norms in the proof of the real Riesz-Thorin interpolation theorem valid in the first quadrant

  • 24.
    Moslehianand, M.S.
    et al.
    Ferdowsi University Mashhad, Centre of Excellence in Analysis on Algebraic Structures, Department of Pure Mathematics, Mashhad.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Reverse Cauchy-Schwarz inequalities for positive C*-valued sesquilinear forms2009In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 12, no 4, p. 701-709Article in journal (Refereed)
    Abstract [en]

    We prove two new reverse Cauchy-Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy-Schwarz inequality due to G. Polya and G. Szego

  • 25.
    Nagy, Károly
    et al.
    College of Nyiregyhaza, Institute of Mathematics and Computer Science, Nyiregyhaza, Institute of Mathematics and Computer Sciences, College of Nyíregyháza.
    Tephnadze, George
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Strong convergence theorem for Walsh-Marcinkiewicz means2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 1, p. 185-195Article in journal (Refereed)
    Abstract [en]

    It is known that the maximal operator ofWalsh-Marcinkiewicz means is bounded from the dyadic martingale Hardy space Hp to the space Lp for p > 2/3 and the condition p > 2/3 is essential. In the case p = 2/3 the boundedness of the maximal operator does not hold. This means that the investigation of the maximal operator at the endpoint case p = 2/3 plays an important role. The main aim of this paper is to prove a strong convergence theorem for the Walsh-Marcinkiewicz means on the Hardy space H2/3.

  • 26.
    Nikolova, Ludmila
    et al.
    Department of Mathematics, Kliment Ohridski University of Sofia.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ushakova, Elena
    Wedestig, Anna
    Weighted Hardy and Pólya-Knopp inequalities with variable limits2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 3, p. 547-557Article in journal (Refereed)
  • 27.
    Oinarov, R.
    et al.
    Faculty of Mathematics and Information Technologies, Eurasian National University, Munaitpasov st., 5, Astana.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Temirkhanova, A.
    Faculty of Mathematics and Information Technologies, Eurasian National University, Munaitpasov st., 5, Astana.
    Weighted inequalities for a class of matrix operators: the case of p≤q2009In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 12, no 4, p. 891-903Article in journal (Refereed)
    Abstract [en]

    We prove a new discrete Hardy-type inequality ||A/||q,u ≤ C||f||p,v, where the matrix operator A is defined by (Af) i:= Σj=1i ai,jfj, ai,j ≥ 0. Moreover, we study die problem of compactness of the operator A, and die dual result is stated

  • 28. Oinarov, Ryskul
    et al.
    Okpoti, Christopher
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Weighted inequalities of Hardy type for matrix operators: the case q2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 4, p. 841-859Article in journal (Refereed)
    Abstract [en]

    Anon-negative triangularmatrix operator is considered in weighted Lebesgue spaces of sequences. Under some additional conditions on the matrix, some new weight characterizations for discrete Hardy type inequalities with matrix operator are proved for the case 1 < q < p < ∞. Some further results are pointed out

  • 29.
    Pecaric, Josip
    et al.
    Faculty of Textile Technology, University of Zagreb.
    Peric, Ivan
    Faculty of Chemical Engineering and Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On sharpness of some integral inequalities and an integral equation of Volterra type2002In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 5, no 4, p. 659-670Article in journal (Refereed)
  • 30.
    Peric, Ivan
    et al.
    University of Zagreb, Faculty of Chemical Engineering and Technology.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wedestig, Anna
    Sharp integral inequalities for C-monotone functions of several variables2000In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 3, no 1, p. 51-62Article in journal (Refereed)
  • 31.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Kufner, Alois
    Mathematical Institute, Czech Academy of Sciences.
    Some difference inequalities with weights and interpolation1998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 437-444Article in journal (Refereed)
    Abstract [en]

    The well-known Grisvard-Jakovlev inequality (see Theorems 1 and 1_ ) can be interpretedas a fractional order Hardy inequality or as a weighted difference inequality. Someinequalities of this type have been recently proved and discussed by the authors and H. Heinig,and this paper coincides mostly with a lecture held by the first author at the International workshopon difference and differential inequalities (July 3 - 7, 1996, Marmara Research Center,Turkey) where some historical remarks, ideas and results from the papers of the authors and H.Heinig have been presented. Additionally we present and prove some new difference inequalitieswith weights. Mostly, we omit the proofs which can be found in the papers mentioned and in thereferences there, and for simplicity, we consider functions on the interval

  • 32.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Popova, Olga V.
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow, Peoples' Friendship University of Russia.
    Stepanov, Vladimir D
    Department of Mathematical Analysis and Function Theory, Peoples Friendship University, Moscow, Computing Centre, Russian Academy of Sciences, Far-Eastern Branch, Khabarovsk, Computing Center, Far Eastern Scientific Center, Russian Academy of Sciences.
    Weighted Hardy-type inequalities on the cone of quasi-concave functions2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 3, p. 879-898Article in journal (Refereed)
    Abstract [en]

    The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz Γ-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters q 1, p > 0 and sufficient conditions for the rest of the range of parameters.

  • 33.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Instituto Superior Tecnico, Research center CEAF.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Quasi-monotone weight functions and their characteristics and applications2012In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 15, no 3, p. 685-705Article in journal (Refereed)
    Abstract [en]

    A weight function w(x) on (0,l) or (l,infinity), is said to be quasi-monotone if w(x)x(-a0) <= C(0)w(y)y(-a0) either for all x <= y or for all y <= x, for some a(0) is an element of R, C-0 >= 1. In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e. g. in interpolation theory, Fourier analysis, Hardy-type inequalities, singular operators and homogenization theory.

  • 34.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Stepanov, Vladimir
    Wall, Peter
    Some scales of equivalent weight characterizations of Hardy's inequality: the case q2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 2, p. 267-279Article in journal (Refereed)
    Abstract [en]

    We consider the weighted Hardy inequality (∫0∞ (∫0x f(t)dt)q u(x)dx)1/q ≤ C(∫0∞ f p(x)v(x)dx)1/p for the case 0 < q < p < ∝, p > 1. The weights u(x) and v(x) for which this inequality holds for all f (x) ≥ 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanov conditions. In this paper, we show that these conditions are not unique and can be supplemented by some continuous scales of conditions and we prove their equivalence. The results for the dual operator which do not follow by duality when 0 < q < 1 are also given

  • 35.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ushakova, Elena
    Some multi-dimensional Hardy type integral inequalities2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 301-319Article in journal (Refereed)
  • 36. Sarybekova, Lyazzat
    et al.
    Tararykova, T.V.
    Tararykova.
    Tleukhanova, N.T.
    L.N. Gumilyov Eurasian National University.
    On a generalization of the Lizorkin theorem on Fourier multipliers2010In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 13, no 3, p. 613-624Article in journal (Refereed)
    Abstract [en]

    A generalization of the Lizorkin theorem on Fourier multipliers is proved. The proofs are based on using the so-called net spaces and interpolation theorems. An example is given of a Fourier multiplier which satisfies the assumptions of the generalized theorem but does not satisfy the assumptions of the Lizorkin theorem.

  • 37. Agarwal, R.P.
    Persson, Lars-Erik
    Zafer, A.
    Selected papers of the international workshop on difference and differential inequalities, Gebze, Kocaeli, Turkey, July 3--7, 19961998In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, no 3, p. 347-461Article in journal (Refereed)
1 - 37 of 37
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