Vector-Valued Weighted Sobolev Spaces with Variable Exponent

Abstract

Our aim is to introduce the vector-valued weighted variable exponent Lebesgue spaces. We discuss two different type of H\"{o}lder 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 weighted variable exponent Sobolev spaces. Finally under some conditions we will investigate some basic properties of vector-valued weighted variable exponent Sobolev spaces.

Keywords

• Vector-valued weighted variable Sobolev spaces,Hölder inequality,Radon-Nikodym property

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