Composition operators on Hardy-Orlicz spaces

Abstract

We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\hat{I}¨$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of $\hat{I}¨$. We introduce an adapted version of Carleson measure. We construct various examples showing that our results are essentially sharp. In the last part, we study the case of Bergman-Orlicz spaces.

78 pages