Remarks on weak compactness criteria in variable exponent Lebesgue spaces

Abstract

We give two weak compactness Andô type criteria in variable exponent Lebesgue spaces Lp(·)(Ω) on infinite measures. This extends some results of [13] given in the case of finite measures. Spaces Lp(·)(Ω) on ininnite measures are weakly Banach-Saks when p+ < 1. Suitable weak compactness criteria in Nakano sequence spaces lpn are also deduced.