Remarks on weak compactness criteria in variable exponent Lebesgue spaces

Abstract

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