Spaces of Holomorphic Functions in the Unit Ball
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ISBN-13:
9780387220369
Veröffentl:
2005
Erscheinungsdatum:
08.02.2005
Seiten:
271
Autor:
Kehe Zhu
Gewicht:
544 g
Format:
243x162x19 mm
Sprache:
Englisch
Beschreibung:
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 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.
Preliminaries.- Bergman Spaces.- The Bloch Space.- Hardy Spaces.- Functions of Bounded Mean Oscillation.- Besov Spaces.- Lipschitz Spaces.
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