Weighted variable exponent amalgam spaces $W(L^{p(x)},L_w^q)$

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) (R n ) and the global component is a weighted Lebesgue space L q w (R n ) .We proceed to show that these Wiener amalgam spaces are Banach function spaces.We also present new Höldertype 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.