《经典傅里叶分析（第3版 英文版）》作品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。

《经典傅里叶分析（第3版 英文版）》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 Lp Spaces and Interpolation

1．1 Lp and Weak Lp

1．1．1 The Distribution Function

1．1．2 Convergence in Measure

1．1．3 A First Glimpse at Interpolation

Exercises

1．2 Convolution and Appromate Identities

1．2．1 Examples of Topological Groups

1．2．2 Convolution

1．2．3 Basic Convolution Inequalities

1．2．4 Appromate Identities

Exercises

1．3 Interpolation

1．3．1 Real Method： The Marcinkiewicz Interpolation Theorem

1．3．2 Complex Method： The Riesz-Thorin Interpolation Theorem

1．3．3 Interpolation of Analytic Families of Operators

Exercises

1．4 Lorentz Spaces

1．4．1 Decreasing Rearrangements

1．4．2 Lorentz Spaces

1．4．3 Duals of Lorentz Spaces

1．4．4 The Off-Diagonal Marcinkiewicz Interpolation Theorem

Exercises

2 Mamal Functions， Fourier Transform， and Distributions

2．1 Mamal Functions

2．1．1 The Hardy-Littlewood Mamal Operator

2．1．2 Control of Other Mamal Operators

2．1．3 Applications to Differentiation Theory

Exercises

2．2 The Schwartz Class and the Fourier Transform

2．2．1 The Class of Schwartz Functions

2．2．2 The Fourier Transform of a Schwartz Function

2．2．3 The Inverse Fourier Transform and Fourier Inversion

2．2．4 The Fourier Transform on L1 + L2

Exercises

2．3 The Class of Tempered Distributions

2．3．1 Spaces of Test Functions

2．3．2 Spaces of Functionals on Test Functions

2．3．3 The Space of Tempered Distributions

Exercises

2．4 More About Distributions and the Fourier Transform

2．4．1 Distributions Supported at a Point

2．4．2 The Laplacian

2．4．3 Homogeneous Distributions

Exercises

2．5 Convolution Operators on Lp Spaces and Multipliers

2．5．1 Operators That Commute with Translations

2．5．2 The Transpose and the Adjoint of a Linear Operator

2．5．3 The Spaces Mp，q（Rn）

2．5．4 Characterizations of M1，1 （Rn） and M2，2 （Rn）

2．5．5 The Space of Fourier Multipliers Mp（Rn）

Exercises

2．6 Oscillatory Integrals

2．6．1 Phases with No Critical Points

2．6．2 Sublevel Set Estimates and the Van der Corput Lemma

Exercises

3 Fourier Series

3．1 Fourier Coefficients

3．1．1 The n-Torus Tn

3．1．2 Fourier Coefficients

3．1．3 The Dirichlet and Fejer Kernels

Exercises

3．2 Reproduction of Functions from Their Fourier Coefficients

3．2．1 Partial sums and Fourier inversion

3．2．2 Fourier series of square summable functions

3．2．3 The Poisson Summation Formula

Exercises

3．3 Decay of Fourier Coefficients

3．3．1 Decay of Fourier Coefficients of Arbitrary Integrable Functions

3．3．2 Decay of Fourier Coefficients of Smooth Functions

4 Topics on Fourier Series

5 Singular Integrals of Convolution Type

6 Littlewood-Paley Theory and Multipliers

7 Weighted Inequalities

AGamma and Beta Functions

BBessel Functions

CRademacher Functions

DSpherical Coordinates

ESome Trigonometric Identities and Inequalities

FSummation by Parts

GBasic Functional Analysis

HThe Minimax Lemma

ITaylor's and Mean Value Theorem in Several Variables

JThe Whitney Deposition of Open Sets in Rn

Glossary

References

Index