前辅文
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 Calderón–Zygmund theory
3.1 The dyadic cubes
3.2 The Calderón–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 kernels
5.4 Exercises
6 BMO and H1
6.1 The BMO space
6.2 The H1(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
