A generalization of the Carleson lemma and weighted norm inequalities for the maximal functions in the Orlicz setting

Abstract

In this note we introduce the notion of Φ-Carleson sequence for Φa convex growth function and provide an equivalent characterization that is an extension of the off-diagonal Carleson embedding lemma. We apply this result to obtain Sawyer-type characterization and two-weight norm estimates for some maximal functions between different Orlicz spaces.