Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics, Vol. 226) (Graduate Texts in Mathematics, 226)

Zhu, Kehe

ISBN 10: 0387220364 / ISBN 13: 9780387220369

Published by Springer, 2005

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Bibliographic Details

• Title: Spaces of Holomorphic Functions in the Unit Ball (Graduate Texts in Mathematics, Vol. 226) (Graduate Texts in Mathematics, 226)
• Publisher: Springer
• Publication Date: 2005
• Language: English
• ISBN 10: 0387220364
• ISBN 13: 9780387220369
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

About the Author

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).