Contents
Preface ix
Chapter 0. Overview 1
Chapter 1. The Bergman Kernel Function 7
1.1. Point-evaluation functionals 7
1.2. Orthonormal bases 9
1.3. Conformal invariance 12
1.4. An extremal problem 14
1.5. Connection with Green's function 16
1.6. The biharmonic Green function 18
Chapter 2. Linear Space Properties 25
2.1. Hardy spaces 25
2.2. Strict and uniform convexity 28
2.3. The Bergman projection 30
2.4. Dual spaces 35
2.5. The pseudohyperbolic metric 38
2.6. The Bloch space ' 43
2.7. Harmonic conjugates 54
2.8. Linear isometries 56
2.9. Function multipliers 59
2.10. Carleson measures 61
2.11. Uniformly discrete sequences 67
Chapter 3. Analytic Properties 73
3.1. More on Hardy spaces 73
3.2. Growth of functions in Bergman spaces 77
3.3. Coefficients of functions in Bergman spaces 81
3.4. Coefficient multipliers 86
3.5. Korenblum's maximum principle 90
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