《奇异积分和函数的可微性(英文版)》是一部讲述奇异积分的教程。奇异积分是数学的三大分支之一分析的最主要和让读者最感兴趣的议题之一，主要研究实数和复数及其函数。《奇异积分和函数的可微性(英文版)》是作者在该领域做出的杰出贡献，这本书的最大成功之处在于在极具传奇色彩表达，将一些鲜为人知的，只有专家才能理解的材料表达的相当具有趣味性，让研究生初级阶段的初学者也可以容易理解。阅读这本书，不仅可以感觉到作者在这方面做出的伟大贡献，更能够激发读者对本学科的向往和积极探索精神。

施泰恩编写的《奇异积分和函数的可微性(英文版)》的应用范围特别广泛，不仅适用于有关专家学者，而且在工程，生物和金融等应用领域有极大的推动作用。

PREFACE

NOTATION

Ⅰ. SOME FUNDAMENTAL NOTIONS OF REAL-VARIABLE THEORY

1. The maximal function

2. Behavior near general points of measurable sets

3. Decomposition in cubes of open sets in R□

4. An interpolation theorem for L□

5. Further results

Ⅱ. SINGULAR INTEGRALS

1. Review of certain aspects of harmonic analysis in R□

2. Singular integrals: the heart of the matter

3. Singular integrals: some extensions and variants of the preceding

4. Singular integral operators which commute with dilations

5. Vector-valued analogues

6. Further results

Ⅲ. RIESZ TRANSFORMS, PORSSON INTEGRALS, AND SPHERICAL HARMONICS

1. The Riesz transforms

2. Poisson integrals and approximations to the identity

3. Higher Riesz transforms and spherical harmonics

4. Further results

Ⅳ. THE LITTLEWOOD-PALEY THEORY AND MULTIPLIERS

1. The Littlewood-Paley g-function

2. The function g□

3. Multipliers (first version)

4. Application of the partial sums operators

5. The dyadic decomposition

6. The Marcinkiewicz multiplier theorem

7. Further results

Ⅴ. DIFFERENTIABILITY PROPERTIES IN TERMS OF FUNCTION SPACES

1. Riesz potentials

2. The Sobolev spaces, L□(R□)

3. Bessel potentials

4. The spaces □ of Lipschitz continuous functions

5. The spaces A□

6. Further results

Ⅵ. EXTENSIONS AND RESTRICTIONS

1. Decomposition of open sets into cubes

2. Extension theorems of Whitney type

3. Extension theorem for a domain with minimally smooth boundary

4. Further results

Ⅶ. RETURN TO THE THEORY OF HARMONIC FUNCTIONS

1. Non-tangential convergence and Fatou's theorem

2. The area integral

3. Application of the theory of H□ spaces

4. Further results

Ⅷ. DIFFERENTIATION OF FUNCTIONS

1. Several notions of pointwise differentiability

2. The splitting of functions

3. A characterization of differentiability

4. Desymmetrization principle

5. Another characterization of differentiability

6. Further results APPENDICES

A. Some Inequalities

B. The Marcinkiewicz Interpolation Theorem

C. Some Elementary Properties of Harmonic Functions

D. Inequalities for Rademacher Functions

BIBLIOGRAPHY

INDEX