Complex Analysis(Stein)
stein functional analysis introduction to further topics in analysis pup 2011
调和分析stein
Elias M. Stein 的上述三部著作均属于 “普林斯顿分析讲义” 系列，其目录与主要内容介绍如下：
Complex Analysis
该书主要介绍复变函数的理论及应用，从复数和复平面讲起，核心是全纯函数性质，同时涉及和其他数学领域的关联内容等。其目录大致如下：
Chapter 1. Preliminaries to Complex Analysis
Complex numbers and the complex plane
Functions on the complex plane
Integration along curves
Chapter 2. Cauchy’s Theorem and Its Applications
Goursat’s theorem
Local existence of primitives and Cauchy’s theorem in a disc
Evaluation of some integrals
Cauchy’s integral formulas
Further applications
Chapter 3. Meromorphic Functions and the Logarithm
5. Homotopies and simply connected domains
6. The complex logarithm
7. Fourier series and harmonic functions
Chapter 9. An Introduction to Elliptic Functions
Liouville’s theorems
The Weierstrass ℘ function
The modular character of elliptic functions and Eisenstein series
Chapter 10. Applications of Theta Functions
Product formula for the Jacobi theta function
The theorems about sums of squares
Appendix A. Asymptotics
Appendix B. Simple Connectivity and Jordan Curve Theorem
Functional Analysis: Introduction to Further Topics in Analysis
其为该系列第四卷，讲述泛函分析基础，并介绍调和分析、概率论、多复变量等领域应用。其目录为：
Chapter 1. Lp Spaces and Banach Spaces
Lp spaces
The case p=∞
Banach spaces
The dual space of Lp when 1≤p<∞
More about linear functionals
Complex Lp and Banach spaces
Appendix: The dual of C(X)
Chapter 2. Lp Spaces in Harmonic Analysis
Early motivations
The Riesz interpolation theorem
The Lp theory of the Hilbert transform
The maximal function and weak-type estimates
The Hardy space Hr1
The space Hr1 and maximal functions
Chapter 3. Distributions: Generalized Functions
Elementary properties
Important examples of distributions
Calderon-Zygmund distributions and Lp estimates
Chapter 4. Applications of the Baire Category Theorem
The Baire category theorem
The uniform boundedness principle
The open mapping theorem
The closed graph theorem
Besicovitch sets
Chapter 5. Rudiments of Probability Theory
Bernoulli trials
The law of large numbers
Conditional expectations
Martingales
Stopping times
Harmonic Analysis
该书聚焦实变理论、极大函数、Hardy 空间、加权不等式、振荡积分及海森堡群相关的调和分析内容等。其目录如下：
Prologue
Part Ⅰ. Real-Variable Theory
Basic assumptions
Examples
Covering lemmas and the maximal function
Generalization of the Calderón-Zygmund decomposition
Singular integrals
Examples of the general theory
Appendix: Truncation of singular integrals
Further results
Part Ⅱ. More about Maximal Functions
Vector-valued maximal functions
Nontangential behavior and Carleson measures
Two applications
Singular approximations of the identity
Further results
Part Ⅲ. Hardy Spaces
Maximal characterization of Hp
Atomic decomposition for Hp
Singular integrals
Appendix: Relation with harmonic function
Further results
Part Ⅳ. H1 and BMO
Part Ⅴ. Weighted Inequalities
Part Ⅵ. Pseudo-differential and Singular Integral Operators: Fourier Integral
Part Ⅶ. Pseudo-differential and Singular Integral
Part Ⅷ. Oscillatory Integrals of the First Kind
Part Ⅸ. Oscillatory Integrals of the Second Kind
Part Ⅹ. Maximal Operators: Some Examples
Part Ⅺ. Maximal Averages and Oscillatory Integrals
Part Ⅻ. Introduction to the Heisenberg Group
Part ⅩⅢ. More about the Heisenberg Group