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

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.