Sub-Bergman spaces in the unit ball of ℂⁿ

Symesak, Frédéric

doi:10.1090/S0002-9939-2010-10437-9

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

Proc. Amer. Math. Soc. 138 (2010), 4405-4411 Request permission

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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