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Spaces of Holomorphic Functions in the Unit Ball

Spaces of Holomorphic Functions in the Unit Ball

Hardcover

Series: Graduate Texts in Mathematics, Book 226

CalculusGeneral Mathematics

ISBN10: 0387220364
ISBN13: 9780387220369
Publisher: Springer Nature
Published: Feb 8 2005
Pages: 271
Weight: 1.20
Height: 0.73 Width: 6.38 Depth: 9.58
Language: English

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.

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Calculus