《现代傅里叶分析（第3版 英文版）》旨在为读者提供学习欧几里得调和解析领域的理论基础，各章有习题及提示。原始版本是以单卷集发布的，但是由于其体积、范围和新材料的增加，第2版改为两卷集发行，新增时频分析和Carleson－Hunt定理等内容。

第3版在第2版的基础上修订新增一些章节，并将加权不等式一章从《现代傅里叶分析》调整到《经典傅里叶分析》，新增若干实例和应用内容，以及一些习题和提示。

1 Smoothness and Function Spaces

1．1 Smooth Functions and Tempered Distributions

1．1．1 Space of Tempered Distributions Modulo Polynomials

1．1．2 Calder6n Reproducing Formula

Exercises

1．2 Laplacian， Riesz Potentials， and Bessel Potentials

1．2．1 Riesz Potentials

1．2．2 Bessel Potentials

Exercises

1．3 Sobolev Spaces

1．3．1 Definition and Basic Properties of General Sobolev Spaces

1．3．2 Littlewood-Paley Characterization of Inhomogeneous

Sobolev Spaces

1．3．3 Littlewood-Paley Characterization of Homogeneous

Sobolev Spaces

Exercises

1．4 Lipschitz Spaces

1．4．1 Introduction to Lipschitz Spaces

1．4．2 Littlewood-Paley Characterization of Homogeneous

Lipschitz Spaces

1．4．3 Littlewood-Paley Characterization of Inhomogeneous

Lipschitz Spaces

Exercises

2 Hardy Spaces， Besov Spaces， and Triebel-Lizorkin Spaces

2．1 Hardy Spaces

2．1．1 Definition of Hardy Spaces

2．1．2 Quasi-norm Equivalence of Several Maximal Functions．．

2．1．3 Consequences of the Characterizations of Hardy Spaces．．

2．1．4 Vector-Valued Hp and Its Characterizations

2．1．5 Singular Integrals on vector-valued Hardy Spaces

Exercises

2．2 Function Spaces and the Square Function Characterization of Hardy

Spaces

2．2．1 Introduction to Function Spaces

2．2．2 Properties of Functions with Compactly Supported Fourier

Transforms

2．2．3 Equivalence of Function Space Norms

2．2．4 The Littlewood-Paley Characterization of Hardy Spaces ．．

Exercises

2．3 Atomic Decomposition of Homogeneous Triebel-Lizorkin

Spaces

2．3．1 Embeddings and Completeness of Triebel-Lizorkin Spaces

2．3．2 The Space of Triebel-Lizorkin Sequences

2．3．3 The Smooth Atomic Decomposition of Homogeneous

Triebel-Lizorkin Spaces

2．3．4 The Nonsmooth Atomic Decomposition of Homogeneous

Triebel-Lizorkin Spaces

2．3．5 Atomic Decomposition of Hardy Spaces

Exercises

2．4 Singular Integrals on Function Spaces

2．4．1 Singular Integrals on the Hardy Space H1

2．4．2 Singular Integrals on Besov-Lipschitz Spaces

2．4．3 Singular Integrals on HP（Rn）

2．4．4 A Singular Integral Characterization of H1 （Rn）

Exercises

3 BMO and Carleson Measures

3．1 Functions of Bounded Mean Oscillation

3．1．1 Definition and Basic Properties of BMO

3．1．2 The John-Nirenberg Theorem

3．1．3 Consequences of Theorem 3．1．6

Exercises

3．2 Duality between H1 and BMO

Exercises

3．3 Nontangential Maximal Functions and Carleson Measures

3．3．1 Definition and Basic Properties of Carleson Measures

3．3．2 BMO Functions and Carleson Measures

Exercises

3．4 The Sharp Maximal Function

3．4．1 Definition and Basic Properties of the Sharp Maximal

Function

3．4．2 A Good Lambda Estimate for the Sharp Function

……