Composition operators on Hardy-Orlicz spaces

Source abstract

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