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.
作者簡介
暫缺《有界解析函數(shù)》作者簡介
圖書目錄
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
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