Mémoires de la Société Mathématique de France 2008; 103 pp; softcover Number: 115 ISBN10: 2856292674 ISBN13: 9782856292679 List Price: US$42 Individual Members: US$37.80 Order Code: SMFMEM/115
 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 socalled 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. Table of Contents  Introduction
 Various special cases
 Preliminaries
 Isomorphism of Bergman spaces
 Several characterizations of \({A^p_\alpha}\)
 Holomorphic Lipschitz spaces
 Pointwise estimates
 Duality
 Integral representations
 Atomic decomposition
 Complex interpolation
 Reproducing kernels
 Carleson type measures
 Coefficient multipliers
 Lacunary series
 Inclusion relations
 Further remarks
 Bibliography
