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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



Sub-Bergman spaces in the unit ball of $ \mathbb{C}^n$

Author: Frédéric Symesak
Journal: Proc. Amer. Math. Soc. 138 (2010), 4405-4411
MSC (2010): Primary 32A36; Secondary 46E22
Published electronically: June 10, 2010
MathSciNet review: 2680064
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Abstract: Let $ \Phi(z)=( \varphi_1(z),\cdots,\varphi_l(z))$ be holomorphic from the unit ball of $ \mathbb{C}^n$ into the unit ball of $ \mathbb{C}^l$. We denote by $ B_{\alpha}(z,w)$ the weighted Bergman kernel. We give a condition for the kernel $ (1-\Phi(z){\overline{\Phi(w)}} )B_{\alpha}(z,w)$ to be a reproducing kernel and we study the related Hilbert space.

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Frédéric Symesak
Affiliation: Laboratoire de Mathématiques et Application, Université de Poitiers, UMR 6086 CNRS, Téléport 2, Boulevard Pierre et Marie Curie, BP30179, 86962 Futuroscope, France

Keywords: Bergman spaces, sub-Hilbert spaces, reproducing kernel
Received by editor(s): November 3, 2009
Received by editor(s) in revised form: February 10, 2010
Published electronically: June 10, 2010
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society

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