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

Author(s): Frédéric Symesak
Journal: Proc. Amer. Math. Soc. 138 (2010), 4405-4411.
MSC (2010): Primary 32A36; Secondary 46E22
Posted: June 10, 2010
MathSciNet review: 2680064
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Abstract | References | Similar articles | Additional information

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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Additional Information:

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
Email: frederic.symesak@univ-poitiers.fr

DOI: 10.1090/S0002-9939-2010-10437-9
PII: S 0002-9939(2010)10437-9
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
Posted: June 10, 2010
Communicated by: Franc Forstneric
Copyright of article: Copyright 2010, American Mathematical Society

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