Composition of operators in Orlicz spaces

Abstract

In this work we find sharp conditions for boundedness on Orlicz spaces of the composition of j operators, each one being of restricted weak type (p,p) for some p > 1, and of strong type (∞, ∞). Particularly, we find necessary and sufficient conditions to obtain modular inequalities for the j-times composition of the Cesàro maximal function of order α. With this approach we treat a kind of strong maximal function related to Cesàro averages over n-dimensional rectangles.