Weighted Variable Exponent Amalgam Spaces W(LP(X),LQW)

Abstract

In the present paper a new family of Wiener amalgam spaces W(LP(X),LQ<inf>W</inf>) is defined, with local component which is a variable exponent Lebesgue space LP(X)(ℝn) and the global component is a weighted Lebesgue space LQ<inf>W</inf>(ℝn). We proceed to show that these Wiener amalgam spaces are Banach function spaces. We also present new Hölder-type inequalities and embeddings for these spaces. At the end of this paper we show that under some conditions the Hardy-Littlewood maximal function is not mapping the space W(LP(X),LQ<inf>W</inf>) into itself.