A DIFFERENT APPROACH TO BOUNDEDNESS OF THE B-MAXIMAL OPERATORS ON THE VARIABLE LEBESGUE SPACES

Abstract

By using the Lp(center dot)-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(center dot). It is noteworthy to mention that our assumption is weaker than uniform Ho center dot lder continuity.