Spaces of Holomorphic Functions in the Unit Ball [electronic resource] / by Kehe Zhu.
By: Zhu, Kehe [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextSeries: Graduate Texts in Mathematics: 226Publisher: New York, NY : Springer New York, 2005Description: X, 274 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387275390.Subject(s): Differential equations, partial  Global analysis (Mathematics)  Several Complex Variables and Analytic Spaces  AnalysisAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.94 Online resources: Click here to access onlineItem type  Current location  Call number  Status  Date due  Barcode  Item holds  

EBOOKS 
ISI Library, Kolkata

Available  EB904 
Preliminaries  Bergman Spaces  The Bloch Space  Hardy Spaces  Functions of Bounded Mean Oscillation  Besov Spaces  Lipschitz Spaces.
There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most wellknown and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993).
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Spaces of holomorphic functions in the unit ball by Zhu Kehe 
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