Browsing Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag) by Author "Persson, Lars Erik"

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; Tidsskriftartikkel; Peer reviewed, 2017) 
Boundedness and compactness of a class of Hardy type operators
Abylayeva, AAkbota M; Oinarov, Ryskul; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 20161213)We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the RiemannLiouville, Hadamard, and ErdelyiKober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and wellknown results are pointed out. 
Fejér and HermiteHadamard Type Inequalities for NQuasiconvex Functions
Abramovich, S; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 20171228)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, 20181114)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 ... 
Hardytype inequalities in fractional hdiscrete calculus
Persson, Lars Erik; Oinarov, Ryskul; Shaimardan, Serikbol (Journal article; Tidsskriftartikkel; Peer reviewed, 20180404)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>≤<! ≤ ></mo> <mi><i>p</i></mi> <mo><</mo> <mn>1</mn> ... 
A new discrete Hardytype inequality with kernels and monotone functions
Kalybay, Aigerim; Persson, Lars Erik; Temirkhanova, Ainur (Peer reviewed, 20151006)A new discrete Hardytype 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 twosided 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; Tidsskriftartikkel; Peer reviewed, 20171208)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 VilenkinNörlund means with nonincreasing coefficients
Memić, Nacima; Persson, Lars Erik; Tephnadze, George; Kroo, A (Peer reviewed, 2016)In [14] we investigated some Vilenkin—Nörlund means with nonincreasing 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 weakL1/(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, 20181127)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, 201701)We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of MatuszewskaOrlicz 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 hardyType Inequalities via Superquadracity
Oguntuase, James A; Persson, Lars Erik; Fabelurin, Olanrewaju O; AdeagboSheikh, Abdulaziz G (Journal article; Tidsskriftartikkel; Peer reviewed, 20171103)Refinements of some limit Hardytype 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 VilenkinFourier series on martingale Hardy spaces
Blahota, Istvan; Nagy, Karoly; Persson, Lars Erik; Tephnadze, George (Journal article; Peer reviewed, 20180920)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 HpLp type inequalities of weighted maximal operators of VilenkinNörlund means and its applications
Baramidze, Lasha; Persson, Lars Erik; Tephnadze, G; Wall, P (Peer reviewed, 20161001)We prove and discuss some new HpLp type inequalities of weighted maximal operators of VilenkinNörlund 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 VilenkinNörlund means. As applications, both some wellknown and new results are pointed out. 
Some inequalities for Cesàro means of double VilenkinFourier series
Tephnadze, G; Persson, Lars Erik (Journal article; Tidsskriftartikkel; Peer reviewed, 20181219)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. 
Some new estimates of the ‘Jensen gap’
Abramovich, Shoshana; Persson, Lars Erik (Peer reviewed, 20160201) 
Some new Hardytype inequalities for RiemannLiouville fractional qintegral operator
Persson, Lars Erik; Shaimardan, Serikbol (Peer reviewed, 20150924)We consider the qanalog of the RiemannLiouville fractional qintegral operator of order n∈Nn∈N. Some new Hardytype inequalities for this operator are proved and discussed. 
Some new Hardytype inequalities in qanalysis
Baiarystanov, A.O.; Persson, Lars Erik; Shaimardan, S.; Temirkhanova, A. (Peer reviewed, 201609)We derive necessary and sufficient conditions (of MuckenhouptBradley type) for the validity of q analogs of (r, p) weighted Hardytype inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardytype inequalities in this new direction. 
Some new TwoSided Inequalities concerning the Fourier Transform
Kopezhanova, Aigerim; Nursultanov, Erlan; Persson, Lars Erik (Journal article; Peer reviewed; Tidsskriftartikkel, 2017)The classical HausdorffYoung and HardyLittlewoodStein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a twosided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).