Now showing items 1-20 of 33

    • Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov kernels 

      Baiarystanov, A.O.; Persson, Lars Erik; Wall, Peter; Abylayeva, A.M. (Journal article; Peer reviewed; Tidsskriftartikkel, 2017)
    • Boundedness and compactness of a class of Hardy type operators 

      Abylayeva, AAkbota M; Oinarov, Ryskul; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2016-12-13)
      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.
    • Equivalent integral conditions related to bilinear Hardy-type inequalities 

      Kanjilal, Saikat; Persson, Lars Erik; Shambilova, Guldarya E (Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
      Infinitely many, even scales of, equivalent conditions are derived to characterize the bilinear Hardy-type inequality under various ranges of parameters.
    • Fejér and Hermite-Hadamard Type Inequalities for N-Quasiconvex Functions 

      Abramovich, S; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-12-28)
      Some new extensions and re finements of Hermite – Hadamard and Fejer type inequalities for functions which are N -quasiconvex are derived and discussed.
    • Geometric Construction of Some Lehmer Means 

      Høibakk, Ralph; Lukkassen, Dag; Meidell, Annette; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-11-14)
      The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0,1 and 2 can be geometrically ...
    • Hardy-type inequalities in fractional h-discrete calculus 

      Persson, Lars Erik; Oinarov, Ryskul; Shaimardan, Serikbol (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-04)
      The first power weighted version of Hardy’s inequality can be rewritten as [<i>mathematical formula</i>] where the constant <i>C</i> =[<i>p</i> / <i>p</i> - <i><b>a</b></i> - 1]<sup><i>p</i></sup> is sharp. This inequality holds in the reversed direction when<math xmlns="http://www.w3.org/1998/Math/MathML"> <mn>0</mn> <mo>&#x2264;<!-- ≤ --></mo> <mi><i>p</i></mi> <mo>&lt;</mo> <mn>1</mn> ...
    • Hardy-type inequalities over balls in R^N for some bilinear and iterated operators 

      Jain, Pankaj; Kanjilal, Saikat; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
      Some new multidimensional Hardy-type inequalites are proved and discussed. The cases with bilinear and iterated operators are considered and some equivalence theorems are proved.
    • Multidimensional Hardy-type inequalities on time scales with variable exponents 

      Fabelurin, Olanrewaju O; Oguntuase, J. A.; Persson, Lars Erik (Journal article; Peer reviewed, 2019)
      A new Jensen inequality for multivariate superquadratic functions is derived and proved. The derived Jensen inequality is then employed to obtain the general Hardy-type integral inequality for superquadratic and subquadratic functions of several variables.
    • A new discrete Hardy-type inequality with kernels and monotone functions 

      Kalybay, Aigerim; Persson, Lars Erik; Temirkhanova, Ainur (Peer reviewed, 2015-10-06)
      A new discrete Hardy-type inequality with kernels and monotone functions is proved for the case 1<q<p<∞1<q<p<∞. This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out.
    • A NEW GENERALIZATION OF BOAS THEOREM FOR SOME LORENTZ SPACES Λq(ω) 

      Kopezhanova, Aigerim; Nursultanov, Erlan; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 2018)
      Let Λq( ω ), q > 0, denote the Lorentz space equipped with the (quasi) norm [<i>MATHEMATICAL FORMULA</I>] for a function f on [0,1] and with ω 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 [<i>MATHEMATICAL FORMULA</I>] and generalized Lorentz Λq( ω ) spaces
    • A new look at classical inequalities involving Banach lattice norms 

      Nikolova, Ludmila; Persson, Lars Erik; Varosanec, Sanja (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-12-08)
      Some 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 ...
    • A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients 

      Memić, Nacima; Persson, Lars Erik; Tephnadze, George; Kroo, A (Peer reviewed, 2016)
      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 ...
    • On geometric construction of some power means 

      Høibakk, Ralph; Lukkassen, Dag; Persson, Lars Erik; Meidell, Annette (Journal article; Peer reviewed, 2018-11-27)
      In the homogenization theory, there are many examples where the effective conductivities of composite structures are power means of the local conductivities. The main aim of this paper is to initiate research concerning geometric construction of some power means of three or more variables. We contribute by giving methods for the geometric construction of the harmonic mean $ P_{-1} $ and the arithmetic ...
    • On Some Power Means and Their Geometric Constructions 

      Høibakk, Ralph; Lukkassen, Dag; Meidell, Annette; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2018)
      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 ...
    • Potential type operators in PDEs and their applications 

      Burtseva, Evgeniya; Lundberg, Staffan; Persson, Lars Erik; Samko, Natasha (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-01)
      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 ℝ<sup>3</sup> 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.
    • Refinements of some limit hardy-Type Inequalities via Superquadracity 

      Oguntuase, James A; Persson, Lars Erik; Fabelurin, Olanrewaju O; Adeagbo-Sheikh, Abdulaziz G (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-03)
      Refinements of some limit Hardy-type inequalities are derived and discussed using the concept of superquadracity. We also proved that all three constants appearing in the refined inequalities obtained are sharp. The natural turning point of our refined Hardy inequality is p=2 and for this case we have even equality.
    • A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces 

      Blahota, Istvan; Nagy, Karoly; Persson, Lars Erik; Tephnadze, George (Journal article; Peer reviewed, 2018-09-20)
      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 to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense.
    • Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications 

      Baramidze, Lasha; Persson, Lars Erik; Tephnadze, G; Wall, P (Peer reviewed, 2016-10-01)
      We prove and discuss some new Hp-Lp type 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.
    • Some Fourier inequalities for orthogonal systems in Lorentz–Zygmund spaces 

      Akishev, Gabdolla; Persson, Lars Erik; Seger, Andreas (Journal article; Peer reviewed, 2019-06-13)
      A number of classical inequalities and convergence results related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of Lorentz–Zygmund spaces.
    • Some inequalities for Cesàro means of double Vilenkin-Fourier series 

      Tephnadze, G; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2018-12-19)
      In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp.