Weighted variable exponent amalgam spaces W(L P(X),L Q W)

Abstract

In the present paper a new family of Wiener amalgam spaces W(L P(X),L Q W) is defined, with local component which is a variable exponent Lebesgue space L P(X)(? n) and the global component is a weighted Lebesgue space L Q W(? n). 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(L P(X),L Q W) into itself.