Spaces of Holomorphic Functions in the Unit Ball
Seiten
2005
|
2005 ed.
Springer-Verlag New York Inc.
978-0-387-22036-9 (ISBN)
Springer-Verlag New York Inc.
978-0-387-22036-9 (ISBN)
Contains many exercises and results. This title is suitable as a graduate text.
The book presents a modern theory of holomorphic function spaces in the open unit ball. 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 proofs 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 book presents a modern theory of holomorphic function spaces in the open unit ball. 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 proofs 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.
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).
Preliminaries.- Bergman Spaces.- The Bloch Space.- Hardy Spaces.- Functions of Bounded Mean Oscillation.- Besov Spaces.- Lipschitz Spaces.
| Reihe/Serie | Graduate Texts in Mathematics ; 226 |
|---|---|
| Zusatzinfo | X, 274 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-387-22036-4 / 0387220364 |
| ISBN-13 | 978-0-387-22036-9 / 9780387220369 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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