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Spaces of Holomorphic Functions in the Unit Ball

Spaces of Holomorphic Functions in the Unit Ball

Paperback

Series: Graduate Texts in Mathematics, Book 226

CalculusGeneral Mathematics

ISBN10: 1441919619
ISBN13: 9781441919618
Publisher: Springer Nature
Published: Nov 10 2010
Pages: 274
Weight: 0.88
Height: 0.60 Width: 6.14 Depth: 9.21
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