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

Ruhan Zhao·Kehe Zhu
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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 $0 -1$. We extend this study in a very natural way to the case where $α$ 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.

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BibTeXRIS

Ruhan Zhao, Kehe Zhu. 2006-11-03. Theory of Bergman Spaces in the Unit Ball of $C^n$. https://arxiv.org/abs/math/0611093

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