Spaces of holomorphic functions in the unit ball

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Spaces of holomorphic functions in the unit ball / Kehe Zhu

資料種別:: 図書
出版情報:: New York : Springer, c2005
形態:: x, 271 p. ; 25 cm
シリーズ名:: Graduate texts in mathematics ; 226 <BA00010074>
著者名:: Zhu, Kehe, 1961- <DA04534958>
ISBN:: 9780387220369 [0387220364]
書誌ID:: BA7148416X

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注記:

Includes bibliographical references (p. [263]-268) and index

主題:

Holomorphic functions; Unit ball

言語:

英語

目次情報:

Preliminaries / 1：

Holomorphic Functions / 1.1：

The Automorphism Group / 1.2：

Lebesgue Spaces / 1.3：

Several Notions of Differentiation / 1.4：

The Bergman Metric / 1.5：

The Invariant Green's Formula / 1.6：

Subharmonic Functions / 1.7：

Interpolation of Banach Spaces / 1.8：

Notes

Exercises

Bergman Spaces / 2：

Bergman Type Projections / 2.1：

Other Characterizations / 2.3：

Carleson Type Measures / 2.4：

Atomic Decomposition / 2.5：

Complex Interpolation / 2.6：

The Bloch Space / 3：

The Bloch space / 3.1：

The Little Bloch Space / 3.2：

Duality / 3.3：

Maximality / 3.4：

Pointwise Multipliers / 3.5：

Hardy Spaces / 3.6：

The Poisson Transform / 4.1：

The Cauchy-Szego Projection / 4.2：

Several Embedding Theorems / 4.4：

Functions of Bounded Mean Oscillation / 4.5：

BMOA / 5.1：

Carleson Measures / 5.2：

Vanishing Carleson Measures and VMOA / 5.3：

BMO in the Bergman Metric / 5.4：

Besov Spaces / 5.6：

The Spaces B[subscript p] / 6.1：

The Minimal Mobius Invariant Space / 6.2：

Mobius Invariance of B[subscript p] / 6.3：

The Dirichlet Space B[subscript 2] / 6.4：

Duality of Besov Spaces / 6.5：

Lipschitz Spaces / 6.6：

B[subscript alpha] Spaces / 7.1：

The Lipschitz Spaces [Lambda subscript alpha] for 0 < [alpha] < 1 / 7.2：

The Zygmund Class / 7.3：

The case [alpha] > 1 / 7.4：

A Unified Treatment / 7.5：

Growth in Tangential Directions / 7.6：

References / 7.7：

Index

Preliminaries / 1：

Holomorphic Functions / 1.1：

The Automorphism Group / 1.2：

Lebesgue Spaces / 1.3：

Several Notions of Differentiation / 1.4：

The Bergman Metric / 1.5：

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