A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces

Kaya, ESRA

doi:10.31801/cfsuasmas.1030942

A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.71, no.3, pp.710-719, 2022 (Peer-Reviewed Journal)

Publication Type: Article / Article
Volume: 71 Issue: 3
Publication Date: 2022
Doi Number: 10.31801/cfsuasmas.1030942
Journal Name: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
Page Numbers: pp.710-719
Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

By using the Lp(⋅)−Lp(⋅)−boundedness of a maximal operator defined on homogeneous space, it has been shown that the B−B−maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the B−B−maximal operator generated by generalized translation operator under a continuity assumption on p(⋅)p(⋅). It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.