本书仅有100多页的篇幅，介绍了一些实分析工具的基础知识，包括：Hardy-Littlewood极大算子、Calderón-Zygmund理论、Littlewood-Paley理论、空间和算子的插值以及H1和BMO空间的基础知识。本书精炼简洁，提供了简要证明和各种难度的练习，旨在挑战和吸引读者。本书是调和分析的导引课程，适用于研究生一年级的Fourier分析和偏微分方程专业。尽管附录中包含了一些背景材料，但读者仍应具备泛函分析的基本知识，了解测度论和积分理论，熟悉Euclid空间中的Fourier变换。
Preface
1 The Hardy-Littlewood maximal operator
1.1 The Hardy-Littlewood operator
1.2 The Lebesgue derivation theorem
1.3 Regular families
1.4 Control of some convolutions
1.5 Exercises
2 Principal values,and some Fourier transforms
2.1 Operators commuting with translations
2.2 Principal values
2.3 Some Fourier transforms
2.4 Homogeneous kernels
2.5 Exercises
3 The Calderon-Zygmund theory
3.1 The dyadic cubes
3.2 The Calder6n-Zygmund decomposition
3.3 Singular integrals
3.4 Exercises
4 The Littlewood-Paley theory
4.1 Vector-valued singular integrals
4.2 The Littlewood-Paley inequalities
4.3 The Marcinkiewicz multiplier theorem
4.4 Exercises
5 Higher Riesz transforms
5.1 Spherical harmonics
5.2 Higher Riesz transforms
5.3 Nonsmooth kemels
5.4 Exercises
6 BMO and H1
6.1 The BMO space
6.2 The Ht(Rn) space
6.3 Duality of H1-BMO
6.4 Exercises
7 Singular integrals on other groups
7.1 The torus
7.2 Z
7.3 Some totally disconnected groups
7.4 Exercises
8 Interpolation
8.1 Real methods
8.2 Complex methods
8.3 Exercises
A Background material
A.1 Vector-valued integrals
A.2 Convolution
A.3 Polar coordinates
A.4 Distribution functions and weak Lp spaces
A.5 Laplace transform
A.6 Khintchine inequalities
A.7 Exercises
B Notation and conventions
B. 1 Glossary of notation and symbols
B.2 Conventions
Postface
Bibliography
Index
