Title: Hardy and Bergman spaces on hyperconvex domains and their composition operators

Authors: Evgeny A. Poletsky and Michael I. Stessin

Issue: Volume 57 (2008), Issue 5, 2153-2202

Abstract: We introduce the scale of weighted Bergman spaces on hyperconvex domains in $\mathbb{C}^n$ and use the Lelong-Jensen formula to prove some fundamental results about these spaces. In particular, generalizations of such classical results as the Littlewood subordination principle, the Littlewood-Paley identity and the change of variables formula are proven. Geometric properties of the introduced norms are revealed by the Nevanlinna counting function associated with a chosen exhaustion. In the last several sections we prove boundedness and compactness results for composition operators generated by holomorphic mappings of hyperconvex domains.