On Weak Compactness of Variable Exponent Spaces

Abstract

This work shows some refined necessary and sufficient conditions placed on the subsets of variable exponent Lebesgue spaces to satisfy the axiom of weak compactness. We also present some results in connection with conditions for all separable variable exponent spaces to be weakly Banach-saks. That is, some results on the Banach-Saks property in variable exponent spaces are given.