Given the Lebesgue space with variable exponent Ls(⋅)(Ω) whose norm is denoted by ||⋅||s(⋅), we show the following equivalence: lim|E|→0||χE||s(⋅)=0 if and only if [Formula presented], where χE is the characteristic function of the measurable set E and |E| its Lebesgue measure. We apply such results to characterize compactness of some inclusions.
Remarks on compactness results for variable exponent spaces Lp(⋅) / Fiorenza, A.; Gogatishvili, A.; Nekvinda, A.; Rakotoson, J. M.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 157:(2022), pp. 136-144. [10.1016/j.matpur.2021.05.012]
Remarks on compactness results for variable exponent spaces Lp(⋅)
Fiorenza A.;
2022
Abstract
Given the Lebesgue space with variable exponent Ls(⋅)(Ω) whose norm is denoted by ||⋅||s(⋅), we show the following equivalence: lim|E|→0||χE||s(⋅)=0 if and only if [Formula presented], where χE is the characteristic function of the measurable set E and |E| its Lebesgue measure. We apply such results to characterize compactness of some inclusions.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
