Hardy operator with variable limits on monotone functions
type: Item
instance of: scholarly article
title: Hardy operator with variable limits on monotone functions
zbMATH Open document ID: 1063.26020
DOI: 10.1155/2003/860547
author: E. P. Ushakova
author: V. D. Stepanov
published in: Journal of Function Spaces and Applications
publication date: 2004-10-28T00:00:00Z
review text: In the paper the authors study the Hardy operator \[ {\mathbb H}f(x)=\int_{a(x)}^{b(x)}f(y)u(y)\,dy \] with a non-negative weight function \(u\), restricted to the cone of non-increasing or non-decreasing non-negative functions on the semiaxis \({\mathbb R}^+:=[0,\infty)\). The border functions \(a(x)\) and \(b(x)\) are supposed to be continuous and strictly increasing on \({\mathbb R}^+\). Using the Sawyer criterion, the boundedness of the generalized Hardy operator with variable limits and the block-diagonal structure of \(\mathbb H\), weighted \(L^p - L^q\) inequalities for the operator \(\mathbb H\) on monotone functions are characterized.
reviewed by: Amiran Gogatishvili
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 2111350
zbMATH Keywords: Hardy operator
zbMATH Keywords: weighted Lebesgue spaces
zbMATH Keywords: weighted integral inequalities
zbMATH Keywords: monotone functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2003/860547
OpenAlex ID: W2037502636
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description: scientific article; zbMATH DE number 2111350