COMPOSITION OPERATORS ON HARDY-ORLICZ AND BERGMAN-ORLICZ SPACES OF THE DISK

We first define analogues of Hardy and Bergman spaces, the Hardy-Orlicz and Bergman-Orlicz spaces attached to an Orlicz function psi. We then study the composition operators on those spaces : they are automatically hounded but their compactness properties, depending on their symbol, also strongly depend on growth conditions on the Orlicz function psi; this leads naturally to a generalized notion of Carleson measure which turns out to be quite relevant in that context, especially when psi grows very rapidly.