A Note on Noneffective Weights in Variable Lebesgue Spaces

A Note on Noneffective Weights in Variable Lebesgue Spaces

We study noneffective weights in the framework of variable exponent Lebesgue spaces, and we show that Lp(⋅)(Ω)=Lωp(⋅)(Ω) if and only if ω(x)1/p(x)~constant in the set where p(⋅)<∞, and ω(x)~constant in the set where p(⋅)=∞.

Bibliographic Details
Main Authors: Alberto Fiorenza, Miroslav Krbec
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2012/853232
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spelling doaj-28809814c9044b2a84c0ffbbdc23351d2020-11-24T22:41:39ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/853232853232A Note on Noneffective Weights in Variable Lebesgue SpacesAlberto Fiorenza0Miroslav Krbec1Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli Federico II, Via Monteoliveto, 3, 80134 Napoli, ItalyInstitute of Mathematics, Academy of Sciences of the Czech Republic, Žitnà 25,115 67 Prague 1, Czech RepublicWe study noneffective weights in the framework of variable exponent Lebesgue spaces, and we show that Lp(⋅)(Ω)=Lωp(⋅)(Ω) if and only if ω(x)1/p(x)~constant in the set where p(⋅)<∞, and ω(x)~constant in the set where p(⋅)=∞.http://dx.doi.org/10.1155/2012/853232
collection DOAJ
language English
format Article
sources DOAJ
author Alberto Fiorenza
Miroslav Krbec
spellingShingle Alberto Fiorenza
Miroslav Krbec
A Note on Noneffective Weights in Variable Lebesgue Spaces
Journal of Function Spaces and Applications
author_facet Alberto Fiorenza
Miroslav Krbec
author_sort Alberto Fiorenza
title A Note on Noneffective Weights in Variable Lebesgue Spaces
title_short A Note on Noneffective Weights in Variable Lebesgue Spaces
title_full A Note on Noneffective Weights in Variable Lebesgue Spaces
title_fullStr A Note on Noneffective Weights in Variable Lebesgue Spaces
title_full_unstemmed A Note on Noneffective Weights in Variable Lebesgue Spaces
title_sort note on noneffective weights in variable lebesgue spaces
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
1758-4965
publishDate 2012-01-01
description We study noneffective weights in the framework of variable exponent Lebesgue spaces, and we show that Lp(⋅)(Ω)=Lωp(⋅)(Ω) if and only if ω(x)1/p(x)~constant in the set where p(⋅)<∞, and ω(x)~constant in the set where p(⋅)=∞.
url http://dx.doi.org/10.1155/2012/853232
work_keys_str_mv AT albertofiorenza anoteonnoneffectiveweightsinvariablelebesguespaces
AT miroslavkrbec anoteonnoneffectiveweightsinvariablelebesguespaces
AT albertofiorenza noteonnoneffectiveweightsinvariablelebesguespaces
AT miroslavkrbec noteonnoneffectiveweightsinvariablelebesguespaces
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