Spaces of holomorphic functions in the unit ball /
"There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known 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...
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| Format: | Book |
| Language: | English |
| Published: |
New York :
Springer,
[2005]
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| Series: | Graduate texts in mathematics ;
226. |
| Subjects: | |
| Online Access: | ebrary MyiLibrary SpringerLink Table of contents Rutgers restricted Contributor biographical information Publisher description |
| Summary: | "There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known 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."--Publisher's website. |
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| Physical Description: | x, 271 pages ; 25 cm |
| Bibliography: | Includes bibliographical references (pages 263-268) and index. |
| ISBN: | 0387220364 9780387220369 1441919619 9781441919618 9780387275390 0387275398 |
| DOI: | 10.1007/0-387-27539-8 |