Vector-Valued Weighted Sobolev Spaces with Variable Exponent

Abstract

Our aim is to introduce the vector-valued weighted variable exponent Lebesgue spaces. We discusstwo different type of Holder inequalities in this spaces. We will also show that every elements of vector-valued ¨weighted variable exponent Lebesgue spaces are locally integrable. Hence we can define vector-valued weightedvariable exponent Sobolev spaces. Finally under some conditions we will investigate some basic properties ofvector-valued weighted variable exponent Sobolev spaces.