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

Year 2022, Volume: 71 Issue: 3, 710 - 719, 30.09.2022

Esra Kaya

https://doi.org/10.31801/cfsuasmas.1030942

Cited By: 1

Abstract

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

Keywords

Maximal operator, singular integrals, variable Lebesgue space

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