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  • 1.
    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 University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, no 3, p. 683-694Article in journal (Refereed)
    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

  • 2.
    Baǐarystanov, Askar O.
    et al.
    Eurasian National University.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. The Artic University of Norway.
    Shaimardan, Serikbol
    Eurasian National University.
    Temirkhanova, Ainur
    Eurasian National University.
    Some new hardy-type inequalities in q-analysis2016In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 10, no 3, p. 761-781Article in journal (Refereed)
    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

  • 3.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norwa.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Multi–dimensional Hardy type inequalities in Hölder spaces2018In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 719-729Article in journal (Refereed)
    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.

  • 4.
    Kopezhanova, Aigerim
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. 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 University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Artic Univ Norway, UiT, Narvik, Norway.
    A new generalization of Boas theorem for some Lorentz spaces lambda(q)(omega)2018In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 619-633Article in journal (Refereed)
    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.

  • 5.
    Kufner, Alois
    et al.
    Mathematical Institute, Academy Sciences of the Czesh Republic.
    Kuliev, K.
    Department of Mathematics, University of West Bohemia.
    Oguntuase, James
    Department of Mathematics, University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Generalized weighted inequality with negative powers2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 1, no 2, p. 269-280Article in journal (Refereed)
    Abstract [en]

    In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case -∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered

  • 6. Oguntuase, James
    et al.
    Okpoti, Christopher
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Allotey, Francis K.A.
    Institute of Mathematical Science, Legon-Accra.
    Mulitdimensional Hardy type inequalities for p2007In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 1, no 1, p. 1-11Article in journal (Refereed)
  • 7.
    Oguntuase, James
    et al.
    Department of Mathematics, University of Agriculture, Abeokuta.
    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 Hardy type inequalities with "broken" exponent p2014In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 8, no 3, p. 405-416Article in journal (Refereed)
    Abstract [en]

    Some new Hardy-type inequalities, where the parameter p is permitted to take different values in different intervals, are proved and discussed. The parameter can even be negative in one interval and greater than one in another. Moreover, a similar result is derived for a multidimensional case.

  • 8.
    Oinarov, Ryskul
    et al.
    Eurasian National University, Astana.
    Temirkhanova, Ainur
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Boundedness and compactness of a class of matrix operators in weighted sequence spaces2008In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 2, no 4, p. 555-570Article in journal (Refereed)
    Abstract [en]

    Characterisations of bounded and compact multiple weighted summation operators from weighted ℓ p into weighted ℓ q spaces are established. Let 1<p,q<∞ , let ℓ p denote the space of all p -summable real sequences, let (ω i,k ) ∞ k=1 for i=1,2,…,n−1 , u=(u i ) ∞ i=1 and v=(v i ) ∞ i=1 be nonnegative sequences, and let ℓ p,v be the space of all sequences f=(f i ) ∞ i=1 such that fv=(f i v i ) ∞ i=1 ∈ℓ p , endowed with the natural norm ∥⋅∥ ℓ p,v defined by (∑ ∞ i=1 |f i v i | p ) 1/p . The n -tuple summation operator S n is defined by (S n f) i =∑ k 1 =1 i ω 1,k 1 ∑ k 2 =1 k 1 ω 2,k 2 ∑ k 3 =1 k 2 ω 3,k 3 ⋯∑ k n−1 =1 k n−2 ω n−1,k n−1 ∑ j=1 k n−1 f j . A necessary and sufficient condition is established for the inequality ∥S n f∥ ℓ q,u ≤C∥f∥ ℓ p,u to hold in the case 1<p≤q<∞ , for all sequences f∈ℓ q,u , where C is an absolute constant. This condition immediately yields a necessary and sufficient condition for S n to be a bounded operator from ℓ q,u into ℓ p,v . This result is a generalisation of a known result by K. F. Andersen and H. P. Heinig in the case n=1 when the operator S n reduces to a discrete Hardy operator of the form (S 1 f) i =∑ i j=1 f j . Finally, a necessary and sufficient condition is established for S n to be a compact operator from ℓ q,u into ℓ p,v when 1<p≤q<∞ . It should be noted that if n=2 then S 2 f can be expressed as a special matrix transformation of the form (Af) i =∑ i j=1 a ij f j .

  • 9.
    Persson, Lars-Erik
    et al.
    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.
    A note on the best constants in some Hardy inequalities2015In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 9, no 2, p. 437-447Article in journal (Refereed)
    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.

  • 10.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tephnadze, George
    Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Some new (Hp,Lp) type inequalities of maximal operators of vilenkin-nörlund means with non-decreasing coefficients2015In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 9, no 4, p. 1055-1069Article in journal (Refereed)
    Abstract [en]

    In this paper we prove and discuss some new (Hp,Lp) type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also apply these inequalities to prove strong convergence theorems of such Vilenkin-Nörlund means. These inequalities are the best possible in a special sense. As applications, both some well-known and new results are pointed out

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