Bounded Analytic Functions
Published on 12. October 1981
466 pages
978-0-08-087412-8 (ISBN)
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Bounded Analytic Functions
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John B. Garnett
Bounded Analytic Functions
Book
01/1981
Saunders College Publishing/Harcourt Brace
€83.08
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Content
- Front Cover
- Bounded Analytic Functions
- Copyright Page
- Contents
- Preface
- Acknowledgments
- List of Symbols
- CHAPTER I. PRELIMINARIES
- 1. Schwarz's Lemma
- 2. Pick's Theorem
- 3. Poisson Integrals
- 4. Hardy-Littlewood Maximal Function
- 5. Nontangential Maximal Function and Fatou's Theorem
- 6. Subharmonic Functions
- Notes
- Exercises and Further Results
- CHAPTER ll. HP SPACES
- 1. Definitions
- 2. Blaschke Products
- 3. Maximal Functions and Boundary Values
- 4. (1/p) f (log|ƒ(t)|/(1 + t2))dt & - 8
- 5. The Nevanlinna Class
- 6. Inner Functions
- 7. Beurling's Theorem
- Notes
- Exercises and Further Results
- CHAPTER lll. CONJUGATE FUNCTIONS
- 1. Preliminaries
- 2. The LP Theorems
- 3. Conjugate Functions and Maximal Functions
- Notes
- Exercises and Further Results
- CHAPTER IV. SOME EXTREMAL PROBLEMS
- 1. Dual Extremal Problems
- 2. The Carleson-Jacobs Theorem
- 3. The Helson-Szegö Theorem
- 4. Interpolating Functions of Constant Modulus
- 5. Parametrization of K
- 6. Nevanlinna's Proof
- Notes
- Exercises and Further Results
- CHAPTER V. SOME UNIFORM ALGEBRA
- 1. Maximal Ideal Spaces
- 2. Inner Functions
- 3. Analytic Discs in Fibers
- 4. Representing Measures and Orthogonal Measures
- 5. The Space L1/H10
- Notes
- Exercises and Further Results
- CHAPTER VI. BOUNDED MEAN OSCILLATION
- 1. Preliminaries
- 2. The John-Nirenberg Theorem
- 3. Littlewood-Paley Integrals and Carleson Measures
- 4. Fefferman's Duality Theorem
- 5. Vanishing Mean Oscillation
- 6. Weighted Norm Inequalities for Maximal Functions and Conjugate Functions
- Notes
- Exercises and Further Results
- CHAPTER VII. INTERPOLATING SEQUENCES
- 1. Carleson's Interpolation Theorem
- 2. The Linear Operator of Interpolation
- 3. Generations
- 4. Harmonic Interpolation
- 5. Earl's Elementary Proof
- Notes
- Exercises and Further Results
- CHAPTER VIII. THE CORONA CONSTRUCTION
- 1. Inhomogeneous Cauchy-Riemann Equations
- 2. The Corona Theorem
- 3. Two Theorems on Minimum Modulus
- 4. Interpolating Blaschke Products
- 5. Carleson's Construction
- 6. Gradients of Bounded Harmonic Functions
- 7. A Constructive Solution of ab/af = µ
- Appendix: The Koszul Complex
- Notes
- Exercises and Further Results
- CHAPTER IX. DOUGLAS ALGEBRAS
- 1. The Douglas Problem
- 2. H8 + C
- 3. The Chang-Marshall Theorem
- 4. The Structure of Douglas Algebras
- 5. The Local Fatou Theorem and an Application
- Notes
- Exercises and Further Results
- CHAPTER X. INTERPOLATING SEQUENCES AND MAXIMAL IDEALS
- 1. Analytic Discs in m
- 2. Hoffman's Theorem
- 3. Approximate Dependence between Kernels
- 4. Interpolating Sequences and Harmonic Separation
- 5. A Constructive Douglas-Rudin Theorem
- Notes
- Exercises and Further Results
- Bibliography
- Index
- Pure and Applied Mathematics
