On Variable Exponent Amalgam Spaces

We derive some of the basic properties of weighted variable exponent Lebesgue spaces L^p(.)_w (ℝⁿ) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W(L^p(.)_w ;L^q_v) is defined, where the local component is a weighted variable exponent Lebesgue space L^p(.)_w (ℝ_n) and the global component is a weighted Lebesgue space L^q_v (ℝ_n) : We investigate the properties of the spaces W(L^p(.)_w ;L^q_v): We also present new Hölder-type inequalities and embeddings for these spaces.