Geometric Qp Functions (Frontiers in Mathematics)

✍ Scribed by Jie Xiao

• Year: 2006
• Tongue: English
• Leaves: 245
• Edition: 1
• Category: Library

✦ Synopsis

This book documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on recent development based on interaction between geometric function and measure theory and other branches of mathematical analysis, including potential theory, harmonic analysis, functional analysis, and operator theory. Largely self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces. Self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.

✦ Table of Contents

3764377623......Page 1
Contents......Page 6
Preface......Page 8
1.1 Background......Page 10
1.2 Logarithmic Conformal Mappings......Page 16
1.3 Conformal Domains and Superpositions......Page 21
1.4 Descriptions via Harmonic Majorants......Page 25
1.5 Regularity for the Euler–Lagrange Equation......Page 28
1.6 Notes......Page 31
2.1 Boundary Value and Brownian Motion......Page 34
2.2 Derivative-free Module via Poisson Extension......Page 38
2.3 Derivative-free Module via Berezin Transformation......Page 41
2.4 Mixture of Derivative and Quotient......Page 44
2.5 Dirichlet Double Integral without Derivative......Page 49
2.6 Notes......Page 54
3.1 Carleson Measures under an Integral Operator......Page 56
3.2 Isomorphism to a Holomorphic Morrey Space......Page 61
3.3 Decomposition via Bergman Style Kernels......Page 66
3.4 Discreteness by Derivatives......Page 73
3.5 Characterization in Terms of a Conjugate Pair......Page 76
3.6 Notes......Page 80
4.1 Nonlinear Integrals and Maximal Operators......Page 82
4.2 Adams Type Dualities......Page 90
4.3 Quadratic Tent Spaces......Page 93
4.4 Preduals under Invariant Pairing......Page 98
4.5 Invariant Duals of Vanishing Classes......Page 105
4.6 Notes......Page 112
5.1 Background on Cauchy Pairing......Page 116
5.2 Cauchy Duality by Dot Product......Page 122
5.3 Atom-like Representations......Page 127
5.4 Extreme Points of Unit Balls......Page 132
5.5 Notes......Page 142
6.1 Hankel and Volterra from Small to Large Spaces......Page 143
6.2 Carleson Embeddings for Dirichlet Spaces......Page 146
6.3 More on Carleson Embeddings for Dirichlet Spaces......Page 152
6.4 Hankel and Volterra on Dirichlet Spaces......Page 158
6.5 Notes......Page 167
7.1 Convexity Inequalities......Page 170
7.2 Exponential Integrabilities......Page 176
7.3 Hadamard Convolutions......Page 184
7.4 Characteristic Bounds of Derivatives......Page 189
7.5 Notes......Page 195
8.1 Basics about Riemann Surfaces......Page 198
8.2 Area and Seminorm Inequalities......Page 202
8.3 Intermediate Setting – BMOA Class......Page 208
8.4 Sharpness......Page 214
8.5 Limiting Case – Bloch Classes......Page 222
8.6 Notes......Page 230
Bibliography......Page 233
T......Page 244
W......Page 245