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

Year 2020, Volume: 6 Issue: 1, 32 - 36, 29.06.2020

Yasin Kaya

https://doi.org/10.23884/mejs.2020.6.1.04

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.

Keywords

Variable exponent Lebesgue space, measure, Radon–Nikodym derivative

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