Spaces of Holomorphic Functions in the Unit Ball
There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA...
Enregistré dans:
| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2005. |
| Collection: | Graduate Texts in Mathematics
226 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Spaces of holomorphic functions in the unit ball, Kehe Zhu, 2005, New York, Springer, 1 vol. (X-271 p.), Graduate Texts in Mathematics, 978-0-387-22036-9 |
| Résumé: | There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993) |
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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9780387275390 |
| ISSN: | 2197-5612 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |