Theory of Bergman Spaces in the Unit Ball of $C^n$

Abstract

There has been a great deal of work done in recent years on weighted Bergman spaces $\apa$ on the unit ball $\bn$ of $\cn$, where $0<p<\infty$ and $\alpha >-1$. We extend this study in a very natural way to the case where $\alpha$ is {\em any} real number and $0<p\le \infty$. This unified treatment covers all classical Bergman spaces, Besov spaces, Lipschitz spaces, the Bloch space, the Hardy space $H^2$, and the so-called Arveson space. Some of our results about integral representations, complex interpolation, coefficient multipliers, and Carleson measures are new even for the ordinary (unweighted) Bergman spaces of the unit disk.

arXiv comment83 pages, revised from 2005 manuscript