An Introduction to Singular Integrals (奇异积分引论) (英文版)

样章

作者：

Jacques Peyrière

定价：

69.00元

ISBN：

978-7-04-052488-8

版面字数：

180.000千字

开本：

16开

全书页数：

暂无

装帧形式：

平装

重点项目：

暂无

出版时间：

1900-01-01

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

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