A Note on Noneffective Weights in Variable Lebesgue Spaces

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(⋅)=∞.