Characterizations of reverse weighted inequalities for maximal operators in Orlicz spaces and Stein's result

Abstract

We give a characterization of reverse type inequalities on weighted Orlicz spaces of the generalized maximal operator MηMη , associated to a Young function ηη , in terms of an appropriated Dini type condition. Our result improves the one given in [3] and, as a consequence, Stein’s result in [10] turns out to be true in more general contexts.