**Contemporary Mathematics**

Volume: 454;
2008;
147 pp;
Softcover

MSC: Primary 30; 32; 46; 47;

Print ISBN: 978-0-8218-4268-3

Product Code: CONM/454

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-0-8218-8133-0
Product Code: CONM/454.E**

List Price: $65.00

Individual Member Price: $52.00

# Banach Spaces of Analytic Functions

Share this page *Edited by *
*Rita A. Hibschweiler; Thomas H. MacGregor*

This volume is focused on Banach spaces of functions analytic in the open
unit disc, such as the classical Hardy and Bergman spaces, and weighted
versions of these spaces. Other spaces under consideration here include the
Bloch space, the families of Cauchy transforms and fractional Cauchy
transforms, BMO, VMO, and the Fock space. Some of the work deals with
questions about functions in several complex variables.

Multiplication operators, composition operators and weighted composition
operators form a central topic of the volume. This topic has been an
extensive area of research for the past twenty years. This volume includes
results characterizing bounded, compact and isometric composition operators
in various settings.

Graduate students who are interested in analysis will find an overview of
current work in the field. Specialists will find interesting questions and
new methods, as well as familiar ideas (such as composition operators) seen
in new settings or in more general form. Mathematicians with an interest in
modern analysis will gain insight into the interplay between function theory
and operator theory which is central to this work.

#### Table of Contents

# Table of Contents

## Banach Spaces of Analytic Functions

- Contents vii8 free
- Preface ix10 free
- A note on the life of Alec Matheson and some of his work 112 free
- On the inverse of an analytic mapping 516
- Isometric composition operators on the Bloch space in the polydisc 920
- Pluripolarity of manifolds 2334
- On a question of Brézis and Korevaar concerning a class of square-summable sequences 3546
- Approximating z in Hardy and Bergman Norms 4354
- A general view of multipliers and composition operators II 6374
- A general view of BMO and VMO 7586
- Order bounded weighted composition operators 93104
- Fractional Cauchy transforms and composition 107118
- Continuous functions in star-invariant subspaces [The Abstract] 117128
- Indestructible Blaschke products 119130
- On Taylor coefficients and multipliers in Fock spaces 135146

#### Readership

Graduate students and research mathematicians interested in function theory and operator theory.