A REVERSE HÖLDER INEQUALITY IN L^p(x)(Ω)

Abstract

In this study, at first we provide a general overview of L^p(x)(Ω) spaces, also known as variable exponent Lebesgue spaces. They are a generalization of classical Lebesgue spaces L^p in the sense that constant exponent replaced by a measurable function. Then, based on classical Lebesgue space approach we prove a reverse of Hölder inequality in L^p(x)(Ω). Therefore, our proof in variable exponent Lebesgue space is very similar to that in classical Lebesgue space.