Geometric Qp Functions Book

Preface     ix
Preliminaries     1
Background     1
Logarithmic Conformal Mappings     7
Conformal Domains and Superpositions     12
Descriptions via Harmonic Majorants     16
Regularity for the Euler-Lagrange Equation     19
Notes     22
Poisson versus Berezin with Generalizations     25
Boundary Value and Brownian Motion     25
Derivative-free Module via Poisson Extension     29
Derivative-free Module via Berezin Transformation     32
Mixture of Derivative and Quotient     35
Dirichlet Double Integral without Derivative     40
Notes     45
Isomorphism, Decomposition and Discreteness     47
Carleson Measures under an Integral Operator     47
Isomorphism to a Holomorphic Morrey Space     52
Decomposition via Bergman Style Kernels     57
Discreteness by Derivatives     64
Characterization in Terms of a Conjugate Pair     67
Notes     71
Invariant Preduality through Hausdorff Capacity     73
Nonlinear Integrals and Maximal Operators     73
Adams Type Dualities     81
Quadratic Tent Spaces     84
Preduals under Invariant Pairing     89
Invariant Duals of Vanishing Classes     96
Notes     103
Cauchy Pairing with Expressions and Extremities     107
Background on Cauchy Pairing     107
Cauchy Duality by Dot Product     113
Atom-like Representations     118
Extreme Points of Unit Balls     123
Notes     133
As Symbols of Hankel and Volterra Operators     135
Hankel and Volterra from Small to Large Spaces     135
Carleson Embeddings for Dirichlet Spaces     138
More on Carleson Embeddings for Dirichlet Spaces     144
Hankel and Volterra on Dirichlet Spaces     150
Notes     159
Estimates for Growth and Decay     163
Convexity Inequalities     163
Exponential Integrabilities     169
Hadamard Convolutions     177
Characteristic Bounds of Derivatives     182
Notes     188
Holomorphic Q-Classes on Hyperbolic Riemann Surfaces     191
Basics about Riemann Surfaces     191
Area and Seminorm Inequalities     195
Intermediate Setting - BMOA Class     201
Sharpness      207
Limiting Case - Bloch Classes     215
Notes     223
Bibliography     227
Index     239