Derivatives characterization of Bergman-Orlicz spaces and applications
Classical Analysis and ODEs
2016-10-07 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1610.01954,
title = {Derivatives characterization of Bergman-Orlicz spaces and applications},
author = {Benoît F. Sehba},
journal= {arXiv preprint arXiv:1610.01954},
year = {2016}
}