本书旨在介绍一维Hardy空间理论，强调近几十年来该领域的重大发展。书中的后七章都致力于最新结果。讲述Hardy空间理论旨在阐述实分析、复分析和抽象分析的相互关系，并将其延伸到欧几里得空间。为了帮助读者更好地学习该教材，每章的结尾都有注、练习和进一步结果。前几节讲述简短的历史评论以引导读者了解本书的原始资料。内容安排结构紧凑合理、文笔优美，证明详尽。本书影响了许多早期杰出的分析学家，培育了一代有复分析和函数代数背景的数学家，对今天该领域的学者也是一本非常经典的参考书。本书被许多美国大学的作为研究生教材。

Ⅰ.PRELIMINARIES

 1.Schwarz's Lemma

 2.Pick's Theorem

 3.Poisson Integrals

 4.Hardy-Littlewood Maximal Function

 5.Nontangential Maximal Function and Fatou's Theorem

 6.Subharmonic Functions

 Notes

 Exercises and Further Results

Ⅱ.Hp SPACES

 1.Definitions

 2.Blaschke Products

 3.Maximal Functions and Boundary Values

 4. (1/π)∫(log If(t)∫/(1 + t2))dt > - ∞

 5.The Nevanlinna Class

 6.Inner Functions

 7.Beurling's Theorem

 Notes

 Exercises and Further Results

Ⅲ.CONJUGATE FUNCITONS

 1.Preliminaries

 2.The Lp Theorems

 3.Conjugate Functions and Maximal Functions

 Notes

 Exercises and Further Results

Ⅳ.SOME EXTREMAL PROBLEMS

 1.Dual Extremal Problems

 2.The Carleson-Jacobs Theorem

 3.The Helson-Szego Theorem

 4.Interpolating Functions of Constant Modulus

 5.Parametxization of K

 6.Nevanlinna's Proof

 Notes

 Exercises and Further Results

Ⅴ.SOME UNIFORM ALGEBRA

 1.Maximal Ideal Spaces

 2.Inner Functions

 3.Analytic Discs in Fibers

 4.Representing Measures and Orthogonal Measures

 5.The Space L1/H1

 Notes

 Exercises and Further Results

Ⅵ.BOUNDED MEAN OSCILLATION

 1.Preliminaries

 2.The John-Nirenberg Theorem

 3.Littlewood-Paley Integrals and Carleson Measures

 4.Fefferman's Duality Theorem

 5.Vanishing Mean Oscillation

 6.Weighted Norm Inequalities

 Notes

 Exercises and Further Results

Ⅶ.INTERPOLATING SEQUENCES

 1.Carleson's Interpolation Theorem

 2.The Linear Operator of Interpolation

 3.Generations

 4.Harmonic Interpolation

 5.Earl's Elementary Proof

 Notes

 Exercises and Further Results

Ⅷ.THE CORONA COMSTRUCTION

 1.Inhomogeneous Cauchy-Riemann Equations

 2.The Corona Theorem

 3.Two Theorems on Minimum Modulus

 4.Interpolating Blaschke Products

 5.Carleson's Construction

 6.Gradients of Bounded Harmonic Functions

 7.A Constructive Solution

 Notes

 Exercises and Further Results

Ⅸ.DOUGLAS ALGEBRAS

 1.The Douglas Problem

 2. H∞ +C

 3.The Chang-Marshall Theorem

 4.The Structure of Douglas Algebras

 5.The Local Fatou Theorem and an Application

 Notes

 Exercises and Further Results

Ⅹ.XINTERPOLATING SEQUENCES AND MAXIMAL IDEALS

 1.Analytic Discs in

 2.Hoffman's Theorem

 3.Approximate Dependence between Kernels

 4.Interpolating Sequences and Harmonic Separation

 5.A Constructive Douglas-Rudin Theorem

 Notes

 Exercises and Further Results

BIBLIOGRAPHY

INDEX