Author | Hedenmalm, Haakan. author |
---|---|
Title | Theory of Bergman Spaces [electronic resource] / by Haakan Hedenmalm, Boris Korenblum, Kehe Zhu |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0497-8 |
Descript | IX, 289 p. online resource |
1 The Bergman Spaces -- 1.1 Bergman Spaces -- 1.2 Some Lp Estimates -- 1.3 The Bloch Space -- 1.4 Duality of Bergman Spaces -- 1.5 Notes -- 1.6 Exercises and Further Results -- 2 The Berezin Transform -- 2.1 Algebraic Properties -- 2.2 Harmonic Functions -- 2.3 Carleson-Type Measures -- 2.4 BMO in the Bergman Metric -- 2.5 A Lipschitz Estimate -- 2.6 Notes -- 2.7 Exercises and Further Results -- 3 Ap -Inner Functions -- 3.1 Ap? -Inner Functions -- 3.2 An Extremal Problem -- 3.3 The Biharmonic Green function -- 3.4 The Expansive Multiplier Property -- 3.5 Contractive Zero Divisors in Ap -- 3.6 An Inner-Outer Factorization Theorem for Ap -- 3.7 Approximation of Subinner Functions -- 3.8 Notes -- 3.9 Exercises and Further Results -- 4 Zero Sets -- 4.1 Some Consequences of Jensenโs Formula -- 4.2 Notions of Density -- 4.3 The Growth Spaces A-? and A-? -- 4.4 A-? Zero Sets, Necessary Conditions -- 4.5 A-? Zero Sets, a Sufficient Condition -- 4.6 Zero Sets for AP? -- 4.7 The Bergman-Nevanlinna Class -- 4.8 Notes -- 4.9 Exercises and Further Results -- 5 Interpolation and Sampling -- 5.1 Interpolation Sequences for AT-? -- 5.2 Sampling Sets for A-? -- 5.3 Interpolation and Sampling in Ap? -- 5.4 Hyperbolic Lattices -- 5.5 Notes -- 5.6 Exercises and Further Results -- 6 Invariant Subspaces -- 6.1 Invariant Subspaces of Higher Index -- 6.2 Inner Spaces in A2? -- 6.3 A Beurling-Type Theorem -- 6.4 Notes -- 6.5 Exercises and Further Results -- 7 Cyclicity -- 7.1 Cyclic Vectors as Outer functions -- 7.2 Cyclicity in Ap Versus in A-? -- 7.3 Premeasures for Functions in A-? -- 7.4 Cyclicity in A-? -- 7.5 Notes -- 7.6 Exercises and Further Results -- 8 Invertible Noncyclic Functions -- 8.1 An Estimate for Harmonic Functions -- 8.2 The Building Blocks -- 8.3 The Basic Iteration Scheme -- 8.4 The Mushroom Forest -- 8.5 Finishing the Construction -- 8.6 Two Applications -- 8.7 Notes -- 8.8 Exercises and Further Results -- 9 Logarithmically Subharmonic Weights -- 9.1 Reproducing Kernels -- 9.2 Green Functions with Smooth Weights -- 9.3 Green Functions with General Weights -- 9.4 An Application -- 9.5 Notes -- 9.6 Exercises and Further Results -- References