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 $(\infty,\infty)$. Particularly, we find necessary and sufficient conditions to obtain modular inequalities for the $j$-times composition of the Cesàro Maximal function of order $\alpha$. With this approach we treat a kind of strong maximal function related to Cesàro averages over $n$-dimensional rectangles.


Published: Rocky Mountain J. Math. 38 (2008), no. 1, 41--59.