Derivatives characterization of Bergman-Orlicz spaces and applications

Abstract: It is well known that a function is in a Bergman space of the unit ball if and only if it satisfies some Hardy-type inequalities. We extend this fact to Bergman-Orlicz spaces. As applications, we obtain Gustavsson-Peetre interpolation of two Bergman-Orlicz spaces and we completely characterize symbols of bounded or compact Ces`aro-type operators on Bergman-Orlicz spaces, extending known results for classical weighted Bergman spaces.