Geometric Qp functions /
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| Author / Creator: | Xiao, Jie, 1963- |
|---|---|
| Imprint: | Basel ; Boston : Birkhàˆuser, c2006. |
| Description: | x, 240 p. ; 24 cm. |
| Language: | English |
| Series: | Frontiers in mathematics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6167609 |
Table of Contents:
- Preface
- 1. Preliminaries
- 1.1. Background
- 1.2. Logarithmic Conformal Mappings
- 1.3. Conformal Domains and Superpositions
- 1.4. Descriptions via Harmonic Majorants
- 1.5. Regularity for the Euler-Lagrange Equation
- 1.6. Notes
- 2. Poisson versus Berezin with Generalizations
- 2.1. Boundary Value and Brownian Motion
- 2.2. Derivative-free Module via Poisson Extension
- 2.3. Derivative-free Module via Berezin Transformation
- 2.4. Mixture of Derivative and Quotient
- 2.5. Dirichlet Double Integral without Derivative
- 2.6. Notes
- 3. Isomorphism, Decomposition and Discreteness
- 3.1. Carleson Measures under an Integral Operator
- 3.2. Isomorphism to a Holomorphic Morrey Space
- 3.3. Decomposition via Bergman Style Kernels
- 3.4. Discreteness by Derivatives
- 3.5. Characterization in Terms of a Conjugate Pair
- 3.6. Notes
- 4. Invariant Preduality through Hausdorff Capacity
- 4.1. Nonlinear Integrals and Maximal Operators
- 4.2. Adams Type Dualities
- 4.3. Quadratic Tent Spaces
- 4.4. Preduals under Invariant Pairing
- 4.5. Invariant Duals of Vanishing Classes
- 4.6. Notes
- 5. Cauchy Pairing with Expressions and Extremities
- 5.1. Background on Cauchy Pairing
- 5.2. Cauchy Duality by Dot Product
- 5.3. Atom-like Representations
- 5.4. Extreme Points of Unit Balls
- 5.5. Notes
- 6. As Symbols of Hankel and Volterra Operators
- 6.1. Hankel and Volterra from Small to Large Spaces
- 6.2. Carleson Embeddings for Dirichlet Spaces
- 6.3. More on Carleson Embeddings for Dirichlet Spaces
- 6.4. Hankel and Volterra on Dirichlet Spaces
- 6.5. Notes
- 7. Estimates for Growth and Decay
- 7.1. Convexity Inequalities
- 7.2. Exponential Integrabilities
- 7.3. Hadamard Convolutions
- 7.4. Characteristic Bounds of Derivatives
- 7.5. Notes
- 8. Holomorphic Q-Classes on Hyperbolic Riemann Surfaces
- 8.1. Basics about Riemann Surfaces
- 8.2. Area and Seminorm Inequalities
- 8.3. Intermediate Setting - BMOA Class
- 8.4. Sharpness
- 8.5. Limiting Case - Bloch Classes
- 8.6. Notes
- Bibliography
- Index
