UID:
almahu_9947366519402882
Format:
1 online resource (277 p.)
ISBN:
1-281-76342-X
,
9786611763428
,
0-08-087351-0
Series Statement:
Pure and applied mathematics
Note:
In title, "p" is superscript".
,
Front Cover; Theory of Hp Spaces, Volume 38; Copyright Page; Contents; Preface; CHAPTER 1. HARMONIC AND SUBHARMONIC FUNCTIONS; 1.1. Harmonic Functions; 1.2. Boundary Behavior of Poisson-Stieltjes Integrals; 1.3. Subharmonic Functions; 1.4. Hardy's Convexity Theorem; 1.5. Subordination; 1.6. Maximal Theorems; Exercises; CHAPTER 2. BASIC STRUCTURE OF HP FUNCTIONS; 2.1. Boundary Values; 2.2. Zeros; 2.3. Mean Convergence to Boundary Values; 2.4. Canonical Factorization; 2.5. The Class N +; 2.6. Harmonic Majorants; Exercises; CHAPTER 3. APPLICATIONS; 3.1. Poisson Integrals and H1
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CHAPTER 8. EXTREMAL PROBLEMS8.1. The Extremal Problem and its Dual; 8.2. Uniqueness of Solutions; 8.3. Counterexamples in the Case p = 1; 8.4. Rational Kernels; 8.5. Examples; Exercises; CHAPTER 9. INTERPOLATION THEORY; 9.1. Universal Interpolation Sequences; 9.2. Proof of the Main Theorem; 9.3. The Proof for p 〈 1; 9.4. Uniformly Separated Sequences; 9.5. A Theorem of Carleson; Exercises; CHAPTER 10. Hp SPACES OVER GENERAL DOMAINS; 10.1. Simply Connected Domains; 10.2. Jordan Domains with Rectifiable Boundary; 10.3. Smirnov Domains; 10.4. Domains not of Smirnov Type
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10.5. Multiply Connected DomainsExercises; CHAPTER 11. Hp SPACES OVER A HALF-PLANE; 11.1. Subharmonic Functions; 11.2. Boundary Behavior; 11.3. Canonical Factorization; 11.4. Cauchy Integrals; 11.5. Fourier Transforms; Exercises; CHAPTER 12. THE CORONA THEOREM; 12.1. Maximal Ideals; 12.2. Interpolation and the Corona Theorem; 12.3. Harmonic Measures; 12.4. Construction of the Contour Γ; 12.5. Arclength of Г; Exercises; Appendix A. Rademacher Functions; Appendix B. Maximal Theorems; References; Author Index; Subject Index; Pure and Applied Mathematics
,
English
Additional Edition:
ISBN 0-12-225150-4
Language:
English
