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

Authors : Esra KAYA

Pages : 710-719

Doi:10.31801/cfsuasmas.1030942

View : 15 | Download : 9

Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :By using the L p insert ignore into journalissuearticles values( ⋅ ); − Lpinsert ignore into journalissuearticles values(⋅);− 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 insert ignore into journalissuearticles values( ⋅ ); pinsert ignore into journalissuearticles values(⋅); . It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.
Keywords : Maximal operator, singular integrals, variable Lebesgue space