On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces
type: Item
instance of: scholarly article
title: On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces
zbMATH Open document ID: 1193.26013
published in: Banach Journal of Mathematical Analysis
publication date: 2010-04-27T00:00:00Z
full work available at URL: https://eudml.org/doc/229007
full work available at URL: tex v4 n1 a4.pdf
review text: Suppose that \(w\) and \(v\) are locally integrable non-negative weight functions. The paper under review studies \(L_p\)-\(L_q\) boundedness of the Hardy-Steklov type operator \(\mathcal{K}\) defined by \[ \mathcal{K}f(x)=w(x)\int_{a(x)}^{b(x)}k(x,y)f(y)v(y)dy, \] where the border functions \(a(x)\) and \(b(x)\) are differentiable and strictly increasing on \((0,\infty)\), \(a(0)=b(0)=0\), \(a(x)<b(x)\) for \(x\in (0,\infty)\), \(a(\infty)=b(\infty)=\infty\), and the kernel \(k(x,y)\) is strictly positive on the set \(\{(x,y):x>0,a(x)<y<b(x)\}\) and satisfies at least one of two generalized Oinarov's conditions \(\mathcal{O}_b\) and \(\mathcal{O}_a\).
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 5702398
zbMATH Keywords: integral operator
zbMATH Keywords: Hardy-Steklov type operator
zbMATH Keywords: boundedness
zbMATH Keywords: weight function
zbMATH Keywords: Oinarov's condition
author: V. D. Stepanov
author: E. P. Ushakova
MaRDI profile type: Publication
OpenAlex ID: W2054950283
DOI: 10.15352/BJMA/1272374670
Recommended article: Boundedness and compactness of a class of Hardy type operators
Recommended article: Boundedness of Hausdorff operators on Lebesgue spaces and Hardy spaces
Recommended article: Boundedness of Stein's square functions associated to operators on Hardy spaces
Recommended article: Q5414354
Recommended article: Boundedness of operators on Hardy spaces
Recommended article: Boundedness of a class of weighted Hardy-Steklov averaging operators
Recommended article: Boundedness and compactness of Hardy-type operators in Banach function spaces
Recommended article: Hardy-Steklov operators and Sobolev-type embedding inequalities
Recommended article: Q5371541
Recommended article: Boundedness and compactness of the Hardy type operator with variable upper limit in weighted Lebesgue spaces
description: scientific article; zbMATH DE number 5702398