本書旨在介紹一維Hardy空間理論，強調近幾十年來該領域的重大發展。書中的後七章都致力於*新結果。講述Hardy空間理論旨在闡述實分析、復分析和抽像分析的相互關繫，並將其延伸到歐幾裡得空間。為了幫助讀者*好地學習該教材，每章的結尾都有注、練習和進一步結果。前幾節講述簡短的歷史評論以引導讀者了解本書的原始資料。內容安排結構緊湊合理、文筆優美，證明詳盡。本書影響了許多早期傑出的分析學家，培育了一代有復分析和函數代數背景的數學家，對**該領域的學者也是一本**經典的參考書。本書被許多美國大學的作為研究生教材。

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