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Cover Art
PRINTED BOOKS
Author Zhu, Kehe, 1961-

Title Spaces of holomorphic functions in the unit ball / Kehe Zhu.

Published New York : Springer, [2005]
©2005

Copies

Location Call No. Status
 UniM ERC  515.732 ZHU    AVAILABLE
Physical description x, 271 pages ; 25 cm.
Series Graduate texts in mathematics ; 226.
Graduate texts in mathematics ; 226.
Bibliography Includes bibliographical references (pages [263]-268) and index.
Contents 1.1 Holomorphic Functions 1 -- 1.2 Automorphism Group 3 -- 1.3 Lebesgue Spaces 9 -- 1.4 Several Notions of Differentiation 17 -- 1.5 Bergman Metric 22 -- 1.6 Invariant Green's Formula 28 -- 1.7 Subharmonic Functions 31 -- 1.8 Interpolation of Banach Spaces 33 -- 2 Bergman Spaces 39 -- 2.1 Bergman Spaces 39 -- 2.2 Bergman Type Projections 43 -- 2.3 Other Characterizations 48 -- 2.4 Carleson Type Measures 56 -- 2.5 Atomic Decomposition 62 -- 2.6 Complex Interpolation 73 -- 3 Bloch Space 79 -- 3.1 Bloch space 79 -- 3.2 Little Bloch Space 89 -- 3.3 Duality 93 -- 3.4 Maximality 94 -- 3.5 Pointwise Multipliers 97 -- 3.6 Atomic Decomposition 98 -- 3.7 Complex Interpolation 103 -- 4 Hardy Spaces 109 -- 4.1 Poisson Transform 109 -- 4.2 Hardy Spaces 122 -- 4.3 Cauchy-Szego Projection 131 -- 4.4 Several Embedding Theorems 141 -- 4.5 Duality 149 -- 5 Functions of Bounded Mean Oscillation 157 -- 5.1 BMOA 157 -- 5.2 Carleson Measures 162 -- 5.3 Vanishing Carleson Measures and VMOA 169 -- 5.4 Duality 172 -- 5.5 BMO in the Bergman Metric 180 -- 5.6 Atomic Decomposition 185 -- 6 Besov Spaces 199 -- 6.1 Spaces B[subscript p] 199 -- 6.2 Minimal Mobius Invariant Space 204 -- 6.3 Mobius Invariance of B[subscript p] 207 -- 6.4 Dirichlet Space B[subscript 2] 210 -- 6.5 Duality of Besov Spaces 216 -- 6.6 Other Characterizations 225 -- 7 Lipschitz Spaces 235 -- 7.1 B[subscript alpha] Spaces 235 -- 7.2 Lipschitz Spaces [Lambda subscript alpha] for 0 < [alpha] < 1 241 -- 7.3 Zygmund Class 246 -- 7.4 Case [alpha] > 1 247 -- 7.5 A Unified Treatment 250 -- 7.6 Growth in Tangential Directions 253 -- 7.7 Duality 257.
Subject Holomorphic functions.
Unit ball.
ISBN 0387220364 (alk. paper)