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内容简介

　　This edition of Bounded Analytic Functions is the same as the first edition exceptfor the corrections of several mathematical and typographical errors. I thank themany colleagues and students who have pointed out errors in the first edition.These include S. Axler， C. Bishop， A. Carbery， K. Dyakonov， J. Handy， V. Havin， H.Hunziker， E Koosis， D. Lubinsky， D. Marshall， R. Mortini， A. Nicolau， M. ONeill，W. Rudin， D. Sarason， D. Suarez， C. Sundberg， C. Thiele， S. Treil， L Uriarte-Tuero，J. Vaisali， N. Varopoulos， and L. Ward.

内页插图

目录

Preface
List of Symbols
Ⅰ. PRELIMINARIES
Schwarzs Lemma
Picks Theorem
Poisson Integrals
Hardy-Littlewood Maximal Function
Nontangential Maximal Function and Fatous Theorem
Subharmonic Functions
Notes
Exercises and Further Results

Ⅱ. Hp SPACES
Definitions
Blaschke Products
Maximal Functions and Boundary Values
(1/π) f(log |f(t)l/(1 + t2))dt > - ∞
The Nevanlinna Class
Inner Functions
Beurlings Theorem
Notes
Exercises and Further Results

Ⅲ. CONJUGATE FUNCTIONS
Preliminaries
The Lp Theorems
Conjugate Functions and Maximal Functions
Notes
Exercises and Further Results

Ⅳ. SOME EXTREMAL PROBLEMS
Dual Extremal Problems
The Carleson-Jacobs Theorem
The Helson-Szeg6 Theorem
Interpolating Functions of Constant Modulus
Parametrization of K
Nevanlinnas Proof
Notes
Exercises and Further Results

Ⅴ. SOME UNIFORM ALGEBRA
Maximal Ideal Spaces
Inner Functions
Analytic Discs in Fibers
Representing Measures and Orthogonal Measures
The Space Ll/Hd
Notes
Exercises and Further Results

Ⅵ. BOUNDED MEAN OSCILLATION
Preliminaries
The John-Nirenberg Theorem
Littlewood-Paley Integrals and Carleson Measures
Feffermans Duality Theorem
Vanishing Mean Oscillation
Weighted Norm Inequalities
Notes
Exercises and Further Results

Ⅶ. INTERPOLATING SEQUENCES
Carlesons Interpolation Theorem
The Linear Operator of Interpolation
Generations
Harmonic Interpolation
Earls Elementary Proof
Notes
Exercises and Further Results

Ⅷ. THE CORONA CONSTRUCTION
Inhomogeneous Cauchy-Riemann Equations
The Corona Theorem
Two Theorems on Minimum Modulus
Interpolating Blaschke Products
Carlesons Construction
Gradients of Bounded Harmonic Functions
A Constructive Solution of
Notes
Exercises and Further Results

Ⅸ. DOUGLAS ALGEBRAS
The Douglas Problem
Hoo + C
The Chang-Marshall Theorem
The Structure of Douglas Algebras
The Local Fatou Theorem and an Application
Notes
Exercises and Further Results

Ⅹ. INTERPOLATING SEQUENCES AND MAXIMAL IDEALS
Analytic Discs in 99l
Hoffmans Theorem
Approximate Dependence between Kernels
Interpolating Sequences and Harmonic Separation
A Constructive Douglas-Rudin Theorem
Notes
Exercises and Further Results
BIBLIOGRAPHY
INDEX

前言/序言

　　This edition of Bounded Analytic Functions is the same as the first edition exceptfor the corrections of several mathematical and typographical errors. I thank themany colleagues and students who have pointed out errors in the first edition.These include S. Axler， C. Bishop， A. Carbery， K. Dyakonov， J. Handy， V. Havin， H.Hunziker， E Koosis， D. Lubinsky， D. Marshall， R. Mortini， A. Nicolau， M. ONeill，W. Rudin， D. Sarason， D. Suarez， C. Sundberg， C. Thiele， S. Treil， L Uriarte-Tuero，J. Vaisali， N. Varopoulos， and L. Ward.
　　I had planned to prepare a second edition with an updated bibliography and anappendix on results new in the field since 1981， but that work has been postponed fortoo long. In the meantime several excellent related books have appeared， includingM. Andersson， Topics in Complex Analysis; G. David and S. Semmes， SingularIntegrals and Rectifiable Sets in Rn and Analysis of and on Uniformly Rectifi-able Sets; S. Fischer， Function theory on planar domains; P. Koosis， Introductionto Hp spaces， Second edition; N. Nikolski， Operators， Functions， and Systems;K. Seip， Interpolation and Sampling in Spaces of Analytic Functions; and B. Simon，Orthogonal Polynomials on the Unit Circle.

有界解析函数（修订版）（英文版） [Bounded Analytic Functions] 电子书 下载 mobi epub pdf txt

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评分☆☆☆☆☆

　　他们不知道我和小巫的关系，说这话时几个人眼睛发亮，诡秘地笑着。我知道通常这种状态是讲话人提出了一种难以实现的愿望，而感到不好意思。我马上安慰他们说：没问题，我一定请到小巫来写。嘴上这样说，心里却想，请她写个序算什么，骗她出来跟这几个她的崇拜者吃顿饭也做得到。出版社的人反复表示，小巫的书做得很好，一开始我明白他们说做得好是指版式啊、宣传啊什么的，后来发现他们是指写得好，我立刻肯定了我对出版社的选择。因为，欣赏小巫的编辑应该是没问题的。

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　　小巫的每一本书都掀起了一股不小的风潮，她的观点成为妈妈们嘴里的新词，改变了一代人的观念，使一代孩子受益。

评分☆☆☆☆☆

　　第一本书是讲母乳的喂养的，那时我的儿子大了，我读这本书是被她书中透出的教育的天赋和人格魅力所吸引。我的书到期了，打算再版，选好出版社后，跟他们谈出版的相关事宜。第一次见面，他们提出的第一件事就是：如果能请到小巫写什么就太好了。

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