Spaces of Holomorphic Functions in the Unit Ball

1. Auflage. Softcover version of original hardcover Auflage 2005
ISBN: 978-1-4419-1961-8
Verlag: Springer

Buch, Englisch, Band 226, 274 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 435 g

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Zhu, Kehe

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preliminaries.- Bergman Spaces.- The Bloch Space.- Hardy Spaces.- Functions of Bounded Mean Oscillation.- Besov Spaces.- Lipschitz Spaces.

Über Autor(innen)

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).