Composition operators on Bergman-Orlicz spaces on the ball

Stéphane Charpentier (1)

1 IMB - Institut de Mathématiques de Bordeaux

We give embedding theorems for weighted Bergman-Orlicz spaces on the ball and then apply our results to the study of composition operators in this context. As one of the motivations of this work, we show that there exist some weighted Bergman-Orlicz spaces, different from $H^{\infinity}$, on which every composition operator is bounded.

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Stéphane Charpentier. Composition operators on Bergman-Orlicz spaces on the ball. 2010. ⟨hal-00495462v2⟩