Weighted Variable Exponent Amalgam Spaces W(LP(x), LWq)

Abstract

In the present paper a new family of Wiener amalgam spaces W(L-p(x), L-w(q)) is defined, with local component which is a variable exponent Lebesgue space L-p(x)(R-n) and the global component is a weighted Lebesgue space L-w(q) (R-n). We proceed to show that these Wiener amalgam spaces are Banach function spaces. We also present new Holder-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(L-p(x), L-w(q)) into itself.