Remarks on weak compactness criteria in variable exponent Lebesgue spaces

Abstract

We give two weak compactness Andô 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 ℓ_pn are also deduced.