调和分析：分析综合教程(第3部分)(影印版)

由Poincare奖获得者 Barry Simon所著的《分析 综合教程》是一套五卷本， 可以作为研究生的分析教科 书，其中包含大量的额外信 息，包括数百道题目和大量 注释，扩展了文中内容并提 供了重要的历史背景。阐述 的深度和广度使得该套图书 成为几乎所有经典分析领域 的宝贵参考资料。 第3部分回到第1部分的 主题，讨论了点态极限（不 仅关注Hardy-Littlewood极 大函数，还包括遍历定理和 鞅收敛）、调和函数和位势 论、标架和小波、空间（包 括有界均值振荡，即BMO） ，在最后一章中，讨论了大 量的不等式，包括Sobolev 空间、Calderon-Zygmund 估计和超压缩半群。 本书可供专业研究人员 （数学家、部分应用数学家 和物理学家）、讲授研究生 阶段分析课程的教师以及在 工作和学习中需要任何分析 学知识的研究生阅读参考。

Preface to the Series Preface to Part 3 Chapter 1.Preliminaries §1.1.Notation and Terminology §1.2.Some Results for Real Analysis §1.3.Some Results from Complex Analysis §1.4.Green's Theorem Chapter 2.Pointwise Convergence Almost Everywhere §2.1.The Magic of Maximal Functions §2.2.Distribution Functions, Weak-L1, and Interpolation §2.3.The Hardy Littlewood Maximal Inequality §2.4.Differentiation and Convolution §2.5.Comparison of Measures §2.6.The Maximal and Birkhoff Ergodic Theorems §2.7.Applications of the Ergodic Theorems §2.8.Bonus Section: More Applications of the Ergodic Theorems §2.9.Bonus Section: Subadditive Ergodic Theorem and Lyapunov Behavior §2.10.Martingale Inequalities and Convergence §2.11.The Christ-Kiselev Maximal Inequality and Pointwise Convergence of Fourier Transforms Chapter 3.Harmonic and Subharmonic Functions §3.1.Harmonic Functions §3.2.Subharmonic Functions §3.3.Bonus Section: The Eremenko-Sodin Proof of Picard's Theorem §3.4.Perron's Method, Barriers, and Solution of the Dirichlet Problem §3.5.Spherical Harmonics §3.6.Potential Theory §3.7.Bonus Section: Polynomials and Potential Theory §3.8.Harmonic Function Theory of Riemann Surfaces Chapter 4.Bonus Chapter: Phase Space Analysis §4.1.The Uncertainty Principle §4.2.The Wavefront Sets and Products of Distributions §4.3.Microlocal Analysis: A First Glimpse §4.4.Coherent States §4.5.Gabor Lattices §4.6.Wavelets Chapter 5.Hp Spaces and Boundary Values of Analytic Functions on the Unit Disk §5.1.Basic Properties of Hp §5.2.H2 §5.3.First Factorization (Riesz) and Hp §5.4.Caratheodory Functions, h1, and the Herglotz Representation §5.5.Boundary Value Measures §5.6.Second Factorization (Inner and Outer Functions) §5.7.Conjugate Functions and M. Riesz's Theorem §5.8.Homogeneous Spaces and Convergence of Fourier Series §5.9.Boundary Values of Analytic Functions in the Upper Half-Plane §5.10.Beurling's Theorem §5.11.HP-Duality and BMO §5.12.Cotlar's Theorem on Ergodic Hilbert Transforms Chapter 6.Bonus Chapter: More Inequalities §6.1.Lorentz Spaces and Real Interpolation