傅里叶变换是在数字信号处理方面很有用的一个方法，在通信和信息专业有很强的应用。本书总结、整理了近50年来傅里叶分析理论研究的基本成果，系统性强，内容先进全面。
作者Loukas Grafakos，希腊雅典人，在加利福尼亚大学洛杉矶分校获得博士学位，现任密苏里州大学数学教授。曾因出色的教学被授予Kemper Fellow奖，自著或与人合著了40篇傅里叶分析方面的文章。
本书内容包括Lp空间和插值，极大函数，傅里叶变换以及广义函数，一维环群上的傅里叶分析，卷积型奇异积分，Littlewood-Paley理论与乘子，光滑性和函数空间，BMO和Carleson测度，非卷积型奇异积分，加权不等式，傅里叶积分的有界性和收剑性。讲述方式易于接受，只要有本科知识就能够阅读，各章节有预备知识提要，习题例题丰富，称得上一本优秀的教材。最后提供了574篇文献目录，读研究人员也很有必要。

出版说明
序
Preface
Chapter 1 Lp Space and Interpolation
1.1 Lp and Week Lp
1.2 Convolution and Approximate Identities
1.3 Interpolation
1.4 Lorentz Space
Chapter 2 Maximal Functions ,Fourier Transform ,and Distributions
2.1 Maximal Functions
2.2 The Schwartz Class and the Fourier Transform
2.3 The Class of Tempered Distributions
2.4 More about Distributions and the Fourier Transform
2.5 Convolution Operators on Lp Spaces and Multipliers
Chapter 3 Fourier Analysis on the Torus 出版说明
序
Preface
Chapter 1 Lp Space and Interpolation
1.1 Lp and Week Lp
1.2 Convolution and Approximate Identities
1.3 Interpolation
1.4 Lorentz Space
Chapter 2 Maximal Functions ,Fourier Transform ,and Distributions
2.1 Maximal Functions
2.2 The Schwartz Class and the Fourier Transform
2.3 The Class of Tempered Distributions
2.4 More about Distributions and the Fourier Transform
2.5 Convolution Operators on Lp Spaces and Multipliers
Chapter 3 Fourier Analysis on the Torus
3.1 Fourier Coefficients
3.2 Decay of Fourier Coefficients
3.3 Pointwise Convergence of Fourier Series
3.4 Divergence of Fourier Series and Bochner-Riesz Summablility
3.5 The Conjugate Function and Convergence in Norm
3.6 Multipliers ,Transference,and Almost Everywhere Convergence
3.7 Lacunary Series
Chapter 4 Singular Integrals of Convolution Type
4.1 The Hibert Transform and the Riesz Transforms
4.2 Homogeneous Singular Integrals and the Method of Rotations
4.3 The Calderon-zygmund Decomposition and Singular Integrals
4.4 Sufficient Conditions for Lp Boundedness
4.5 Vector-Valued Inequalities
4.6 Vector-Valued Singular Integrals
Chapter 5 Little wood-paley Theory and Multipliers
5.1 Little wood-paley Theory
5.2 Two Multiplier Therrems
5.3 Applications of Little wood-paley Theory
5.4 The Haar System,Conditional Expectation,and Martingales
5.5 The Spherical Maximal Function
5.6 Wavelets
Chapter 6 Smoothness and Function Spaces
6.1 Riesz Potentials ,Bessel Potentials ,and Fractional Integrals
6.2 Sobolev Spaces
6.3 Lipschitz Spaces
6.4 Hardy Spaces
6.5 Besov-Lipschitz and Triebel-Lizorkin Spaces
6.6 Atomic Decomposition
6.7 Singular Integrals on Function Spaces
Chapter 7 BMO and Carleson Measures
7.1 Functions of Bounded Mean Oscillation
7.2 Duality Between H1 and Carleson Measures
7.3 Nontangential Maximal Functions and Carleson Measures
……
Chapter 8 Singular Integrals of Nonconvolution Type
Chapter 9 Weighted Intequalities
Chapter 10 Boundedness and Convergence of Fourier Integrals
Appendix A Gamma and Beta Functions
Appendix B Bessel Functions
Appendix C Rademacher Functions
Appendix D Spherical Coordinates
Appendix E Some Trigonometric Identities and Inequalities
Appendix F Summation by Parts
Appendix G Basic Functional Analysis
Appendix H The Minimax Lemma
Appendix I The Schur Lemma
Appendix J The Whitney Decomposition of open sets in Rn
Appendix K Smoothness and Vanishing Moments
Bibliography
Index of Notation
Index
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