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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 853232, 5 pages
http://dx.doi.org/10.1155/2012/853232
Research Article

A Note on Noneffective Weights in Variable Lebesgue Spaces

1Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli Federico II, Via Monteoliveto, 3, 80134 Napoli, Italy
2Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sezione di Napoli, Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111, 80131 Napoli, Italy
3Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitnà 25,115 67 Prague 1, Czech Republic

Received 5 June 2011; Accepted 22 September 2011

Academic Editor: Pankaj Jain

Copyright © 2012 Alberto Fiorenza and Miroslav Krbec. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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()=.