**Memoires de la Societe Mathematique de France**

Volume: 115;
2008;
103 pp;
Softcover

MSC: Primary 32;
**Print ISBN: 978-2-85629-267-9
Product Code: SMFMEM/115**

List Price: $42.00

AMS Member Price: $33.60

# Theory of Bergman Spaces in the Unit Ball of \(\mathbb{C}^{n}\)

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*Ruhan Zhao; Kehe Zhu*

A publication of the Société Mathématique de France

There has been a great deal of work done in recent years on weighted Bergman spaces \(A^p_\alpha\) on the unit ball \({\mathbb B}_n\) of \({\mathbb C}^n\), where \(0 < p < \infty\) and \(\alpha>-1\). The authors extend this study in a very natural way to the case where \(\alpha\) is 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 the results about integral representations, complex interpolation, coefficient multipliers, and Carleson measures are new even for the ordinary (unweighted) Bergman spaces of the unit disk.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in analysis.