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

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Middle East Journal of Science
Volume:6 Issue:1
A REVERSE HÖLDER INEQUALITY IN L^p(x)(Ω)

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

Pages : 32-36

View : 45 | Download : 8

Publication Date : 2020-06-29

Article Type : Research Paper

Abstract :In this study, at first we provide a general overview of L^pinsert ignore into journalissuearticles values(x);insert ignore into journalissuearticles values(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^pinsert ignore into journalissuearticles values(x);insert ignore into journalissuearticles values(Ω); . Therefore, our proof in variable exponent Lebesgue space is very similar to that in classical Lebesgue space.
Keywords : Variable exponent Lebesgue space, measure, RadonNikodym derivative

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