Banach Spaces of Analytic Functions: AMS Special Session, April 22-23, 2006, University of New Hampshire, Durham, New Hampshire

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Rita A. Hibschweiler, Thomas H. MacGregor
American Mathematical Soc., 2008 - Mathematics - 147 pages
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.

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A note on the life of Alec Matheson and some of his work
On the inverse of an analytic mapping
Isometric composition operators on the Bloch space in the polydisc
Pluripolarity of manifolds
On a question of Brézis and Korevaar concerning a class of squaresummable sequences
Approximating z in Hardy and Bergman Norms
A general view of multipliers and composition operators II
A general view of BMO and VMO
Order bounded weighted composition operators
Fractional Cauchy transforms and composition
Continuous functions in starinvariant subspaces The Abstract
Indestructible Blaschke products
On Taylor coefficients and multipliers in Fock spaces

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