Spaces of Holomorphic Functions in the Unit Ball [electronic resource] / by Kehe Zhu.

By: Zhu, Kehe [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Graduate Texts in Mathematics: 226Publisher: New York, NY : Springer New York, 2005Description: X, 274 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387275390Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Functions of complex variables | Mathematics | Several Complex Variables and Analytic Spaces | AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515.94 LOC classification: QA331.7Online resources: Click here to access online
Contents:
Preliminaries -- Bergman Spaces -- The Bloch Space -- Hardy Spaces -- Functions of Bounded Mean Oscillation -- Besov Spaces -- Lipschitz Spaces.
In: Springer eBooksSummary: 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. 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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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 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. 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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