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 Cesaro Maximal function of order $\alpha$. With this approach we treat a kind of strong maximal function related to Cesaro averages over $n$-dimensional rectangles. Published: Rocky Mountain J. Math. 38 (2008), no. 1, 41--59.
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