有界解析函数

Preface

List of Symbols

Ⅰ. PRELIMINARIES

Schwarzs Lemma

Picks Theorem

Poisson Integrals

Hardy-Littlewood Maximal Function

Nontangential Maximal Function and Fatous Theorem

Subharmonic Functions

Notes

Exercises and Further Results

Ⅱ. Hp SPACES

Definitions

Blaschke Products

Maximal Functions and Boundary Values

(1/π) f(log |f(t)l/(1 + t2))dt > - ∞

The Nevanlinna Class

Inner Functions

Beurlings Theorem

Notes

Exercises and Further Results

Ⅲ. CONJUGATE FUNCTIONS

Preliminaries

The Lp Theorems

Conjugate Functions and Maximal Functions

Notes

Exercises and Further Results

Ⅳ. SOME EXTREMAL PROBLEMS

Dual Extremal Problems

The Carleson-Jacobs Theorem

The Helson-Szeg6 Theorem

Interpolating Functions of Constant Modulus

Parametrization of K

Nevanlinnas Proof

Notes

Exercises and Further Results

Ⅴ. SOME UNIFORM ALGEBRA

Maximal Ideal Spaces

Inner Functions

Analytic Discs in Fibers

Representing Measures and Orthogonal Measures

The Space Ll/Hd

Notes

Exercises and Further Results

Ⅵ. BOUNDED MEAN OSCILLATION

Preliminaries

The John-Nirenberg Theorem

Littlewood-Paley Integrals and Carleson Measures

Feffermans Duality Theorem

Vanishing Mean Oscillation

Weighted Norm Inequalities

Notes

Exercises and Further Results

Ⅶ. INTERPOLATING SEQUENCES

Carlesons Interpolation Theorem

The Linear Operator of Interpolation

Generations

Harmonic Interpolation

Earls Elementary Proof

Notes

Exercises and Further Results

Ⅷ. THE CORONA CONSTRUCTION

Inhomogeneous Cauchy-Riemann Equations

The Corona Theorem

Two Theorems on Minimum Modulus

Interpolating Blaschke Products

Carlesons Construction

Gradients of Bounded Harmonic Functions

A Constructive Solution of

Notes

Exercises and Further Results

Ⅸ. DOUGLAS ALGEBRAS

The Douglas Problem

Hoo + C

The Chang-Marshall Theorem

The Structure of Douglas Algebras

The Local Fatou Theorem and an Application

Notes

Exercises and Further Results

Ⅹ. INTERPOLATING SEQUENCES AND MAXIMAL IDEALS

Analytic Discs in 99l

Hoffmans Theorem

Approximate Dependence between Kernels

Interpolating Sequences and Harmonic Separation

A Constructive Douglas-Rudin Theorem

Notes

Exercises and Further Results

BIBLIOGRAPHY

INDEX

This edition of Bounded Analytic Functions is the same as the first edition exceptfor the corrections of several mathematical and typographical errors. I thank themany colleagues and students who have pointed out errors in the first edition.These include S. Axler， C. Bishop， A. Carbery， K. Dyakonov， J. Handy， V. Havin， H.Hunziker， E Koosis， D. Lubinsky， D. Marshall， R. Mortini， A. Nicolau， M. ONeill，W. Rudin， D. Sarason， D. Suarez， C. Sundberg， C. Thiele， S. Treil， L Uriarte-Tuero，J. Vaisali， N. Varopoulos， and L. Ward.