Theory of H[superscript p] spaces

by Peter L. Duren (Editor)

Overview

The theory of HP spaces has its origins in discoveries made forty or fifty years ago by such mathematicians as G. H. Hardy, J. E. Littlewood, I. I. Privalov, F. and M. Riesz, V. Smirnov, and G. Szego. Most of this early work is concerned with the properties of individual functions of class HP, and is classical in spirit. In recent years, the development of functional analysis has stimulated new interest in the HP classes as linear spaces. This point of view has suggested a variety of natural problems and has provided new methods of attack, leading to important advances in the theory.

This book is an account of both aspects of the subject, the classical and the modern. It is intended to provide a convenient source for the older parts of the theory (the work of Hardy and Littlewood, for example), as well as to give a self-contained exposition of more recent developments such as Beurling’s theorem on invariant subspaces, the Macintyre-RogosinskiShapiro-Havinson theory of extremal problems, interpolation theory, the dual space structure of HP with p < 1, HP spaces over general domains, and Carleson’s proof of the corona theorem. Some of the older results are proved by modern methods. In fact, the dominant theme of the book is the interplay of “ hard" and “ soft" analysis, the blending of classical and modern techniques and viewpoints.

Product Details

ISBN-13:	9780080873510
Publisher:	Elsevier Science
Publication date:	07/31/1970
Series:	ISSN , #38
Sold by:	Barnes & Noble
Format:	eBook
Pages:	260
Sales rank:	309,825
File size:	5 MB

Table of Contents

Dedication

Preface

Chapter 1: Harmonic and Subharmonic Functions

Chapter 2: Basic Structure of Hp Functions

Chapter 3: Applications

Chapter 4: Conjugate Functions

Chapter 5: Mean Growth and Smoothness

Chapter 6: Taylor Coefficients

Chapter 7: Hp as a Linear Space

Chapter 8: Extremal Problems

Chapter 9: Interpolation Theory

Chapter 10: Hp Spaces Over General Domains

Chapter 11: Hp Spaces Over A Half-Plane

Chapter 12: The Corona Theorem

Appendix A: Rademacher Functions

Appendix B: Maximal Theorems

References

Author Index

Pure and Applied Mathematics