On a weighted inequality of Hardy type in spaces \(L^{p(\cdot)}\)
type: Item
instance of: scholarly article
title: On a weighted inequality of Hardy type in spaces \(L^{p(\cdot)}\)
zbMATH Open document ID: 1172.26006
author: Farman I. Mamedov
author: Aziz Harman
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-13T00:00:00Z
review text: The boundedness of the Hardy type operator \(Hf(x) = \int_{\{t\in \mathbb R^ n :|t| \leq |x|\}}f(t)\,dt\) in weighted variable exponent Lebesgue spaces \(L^{p(.)}\) is studied. In particular, necessary and sufficient conditions are established on the weight functions \(v(x), w(x)\) and the exponents \(p(x), q(x)\) for which the inequality \[ \|v^{\frac1{q(x)}}Hf(x)\|_{q(.)} \leq C\| w^{\frac1{p(x)}}f(x)\|_{p(.)} \] is valid. An application of the result obtained to power weights is also given.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5553633
zbMATH Keywords: Hardy operator
zbMATH Keywords: Hardy inequality
zbMATH Keywords: variable exponents
zbMATH Keywords: weighted inequality
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.029
OpenAlex ID: W1994567320
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DOI: 10.1016/J.JMAA.2008.12.029
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description: scientific article; zbMATH DE number 5553633