Weighted Hardy and potential operators in the generalized Morrey spaces
type: Item
instance of: scholarly article
title: Weighted Hardy and potential operators in the generalized Morrey spaces
zbMATH Open document ID: 1211.42018
author: Lars-Erik Persson
author: Natasha Samko
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-03-08T00:00:00Z
full work available at URL: http://hdl.handle.net/10400.1/11731
review text: The authors study the weighted \(p\rightarrow q\)-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces \(\mathcal L^{p,\varphi }(\mathbb R^n, w)\) defined by an almost increasing function \(\varphi (r)\) and radial type weight \(w(|x|)\) from the Bary-Stechkin-type class. Sufficient conditions are obtained, in terms of some integral inequalities imposed on \(\varphi \) and \(w\), for such a \(p\rightarrow q\)-boundedness. In the case of local spaces the obtained conditions are also necessary. These results are applied to derive a similar weighted \(p\rightarrow q\)-boundedness of the Riesz potential operator.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47G40
zbMATH DE Number: 5862730
zbMATH Keywords: generalized Morrey spaces
zbMATH Keywords: weighted Hardy operator
zbMATH Keywords: weighted Hardy inequalities
zbMATH Keywords: Riesz potential operator
zbMATH Keywords: Bary-Stechkin classes
zbMATH Keywords: Matuszewska-Orlicz indices
reviewed by: Lubomira Softova
MaRDI profile type: Publication
OpenAlex ID: W2038550552
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DOI: 10.1016/J.JMAA.2010.11.029
description: scientific article; zbMATH DE number 5862730