New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Theory of Bergman Spaces in the Unit Ball of $$\mathbb{C}^n$$
 Mémoires de la Société Mathématique de France 2008; 103 pp; softcover Number: 115 ISBN-10: 2-85629-267-4 ISBN-13: 978-2-85629-267-9 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 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. 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