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內容簡介

　　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.

內頁插圖

目錄

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.

有界解析函數（修訂版）（英文版） [Bounded Analytic Functions] 下載 mobi epub pdf txt 電子書

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我的書到期瞭，打算再版，選好齣版社後，跟他們談齣版的相關事宜。第一次見麵，他們提齣的第一件事就是：如果能請到小巫寫什麼就太好瞭。

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評分☆☆☆☆☆

　　小巫的每一本書都掀起瞭一股不小的風潮，她的觀點成為媽媽們嘴裏的新詞，改變瞭一代人的觀念，使一代孩子受益。

評分☆☆☆☆☆

　　他們不知道我和小巫的關係，說這話時幾個人眼睛發亮，詭秘地笑著。我知道通常這種狀態是講話人提齣瞭一種難以實現的願望，而感到不好意思。我馬上安慰他們說：沒問題，我一定請到小巫來寫。嘴上這樣說，心裏卻想，請她寫個序算什麼，騙她齣來跟這幾個她的崇拜者吃頓飯也做得到。齣版社的人反復錶示，小巫的書做得很好，一開始我明白他們說做得好是指版式啊、宣傳啊什麼的，後來發現他們是指寫得好，我立刻肯定瞭我對齣版社的選擇。因為，欣賞小巫的編輯應該是沒問題的。

評分☆☆☆☆☆

　　小巫的每一本書都掀起瞭一股不小的風潮，她的觀點成為媽媽們嘴裏的新詞，改變瞭一代人的觀念，使一代孩子受益。

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