Composition operators on Hardy-Orlicz spaces

Details Composition operators on Hardy-Orlicz spaces Composition operators on Hardy-Orlicz spaces

2006-10-29

arxiv.org/abs/math/0610905v1

Mathematics

Functional Analysis

78 pages

Scientific paper

We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\Psi$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of $\Psi$. 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.

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