《有界解析函式(修訂版)(英文版)》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. O'Neill,W. Rudin, D. Sarason, D. Suarez, C. Sundberg, C. Thiele, S. Treil, L Uriarte-Tuero,J. Vaisali, N. Varopoulos, and L. Ward.
基本介紹
- 書名：有界解析函式
- 作者：加耐特(John B.Garnett)
- 出版日期：2010年1月1日
- 語種：英語
- ISBN：7510005469, 9787510005466
- 外文名：Bounded Analytic Functions
- 出版社：世界圖書出版公司
- 頁數：459頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
內容簡介,圖書目錄,序言,
內容簡介
《有界解析函式(修訂版)(英文版)》是由世界圖書出版公司出版的。
圖書目錄
Preface
List of Symbols
Ⅰ. PRELIMINARIES
Schwarz's Lemma
Pick's Theorem
Poisson Integrals
Hardy-Littlewood Maximal Function
Nontangential Maximal Function and Fatou's 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
Beurling's 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
Nevanlinna's 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
Fefferman's Duality Theorem
Vanishing Mean Oscillation
Weighted Norm Inequalities
Notes
Exercises and Further Results
Ⅶ. INTERPOLATING SEQUENCES
Carleson's Interpolation Theorem
The Linear Operator of Interpolation
Generations
Harmonic Interpolation
Earl's 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
Carleson's 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
Hoffman's Theorem
Approximate Dependence between Kernels
Interpolating Sequences and Harmonic Separation
A Constructive Douglas-Rudin Theorem
Notes
Exercises and Further Results
BIBLIOGRAPHY
INDEX
List of Symbols
Ⅰ. PRELIMINARIES
Schwarz's Lemma
Pick's Theorem
Poisson Integrals
Hardy-Littlewood Maximal Function
Nontangential Maximal Function and Fatou's 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
Beurling's 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
Nevanlinna's 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
Fefferman's Duality Theorem
Vanishing Mean Oscillation
Weighted Norm Inequalities
Notes
Exercises and Further Results
Ⅶ. INTERPOLATING SEQUENCES
Carleson's Interpolation Theorem
The Linear Operator of Interpolation
Generations
Harmonic Interpolation
Earl's 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
Carleson's 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
Hoffman's Theorem
Approximate Dependence between Kernels
Interpolating Sequences and Harmonic Separation
A Constructive Douglas-Rudin Theorem
Notes
Exercises and Further Results
BIBLIOGRAPHY
INDEX
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. O'Neill,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.
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.
