Description
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 viewhas 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.
Table of Contents
DedicationPrefaceChapter 1: Harmonic and Subharmonic FunctionsChapter 2: Basic Structure of Hp FunctionsChapter 3: ApplicationsChapter 4: Conjugate FunctionsChapter 5: Mean Growth and SmoothnessChapter 6: Taylor CoefficientsChapter 7: Hp as a Linear SpaceChapter 8: Extremal ProblemsChapter 9: Interpolation TheoryChapter 10: Hp Spaces Over General DomainsChapter 11: Hp Spaces Over A Half-PlaneChapter 12: The Corona TheoremAppendix A: Rademacher FunctionsAppendix B: Maximal TheoremsReferencesAuthor IndexPure and Applied Mathematics
