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

Authors : Yasin KAYA

Pages : 32-36

Doi:10.23884/mejs.2020.6.1.04

View : 9 | Download : 6

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