Some \(s\)-numbers of an integral operator of Hardy type on \(L^{p(\cdot)}\) spaces
type: Item
instance of: scholarly article
title: Some \(s\)-numbers of an integral operator of Hardy type on \(L^{p(\cdot)}\) spaces
zbMATH Open document ID: 1175.47017
published in: Journal of Functional Analysis
publication date: 2009-06-30T00:00:00Z
review text: The Hardy-type operator \(Tf(x)=\int_a^x f(t)\,dt\), \(x \in I=[a,b]\), is studied in the space \(L^{p (\cdot)} (I)\), where \(p (\cdot)\) is a variable exponent satisfying certain conditions. The following estimate is established for the relevant \(n\)th approximation number \(s_n\): \[ \lim\limits_{n\to\infty} ns_n=\frac{1}{2\pi}\int_I [p'(t) p(t) ^{p(t)-1}]^{1/p(t)} \sin (\pi/p(t))\,dt, \] where \(p'(t)=p(t)/(p(t)-1)\).
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 5572192
zbMATH Keywords: Hardy-type operator
zbMATH Keywords: compactness
zbMATH Keywords: \(s\)-numbers
zbMATH Keywords: variable exponent function spaces
author: D. E. Edmunds
author: Jan Lang
author: Aleš Nekvinda
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.02.015
OpenAlex ID: W2105409896
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DOI: 10.1016/J.JFA.2009.02.015
description: scientific article; zbMATH DE number 5572192