03019nam a22004695i 4500
978-0-387-27539-0
DE-He213
20180115171353.0
cr nn 008mamaa
100301s2005 xxu| s |||| 0|eng d
9780387275390
978-0-387-27539-0
10.1007/0-387-27539-8
doi
QA331.7
PBKD
bicssc
MAT034000
bisacsh
515.94
23
Zhu, Kehe.
author.
Spaces of Holomorphic Functions in the Unit Ball
[electronic resource] /
by Kehe Zhu.
New York, NY :
Springer New York,
2005.
X, 274 p.
online resource.
text
txt
rdacontent
computer
c
rdamedia
online resource
cr
rdacarrier
text file
PDF
rda
Graduate Texts in Mathematics,
0072-5285 ;
226
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).
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Functions of complex variables.
Mathematics.
Several Complex Variables and Analytic Spaces.
Analysis.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9780387220369
Graduate Texts in Mathematics,
0072-5285 ;
226
http://dx.doi.org/10.1007/0-387-27539-8
ZDB-2-SMA
369325
369325
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK