Abstract
Let Φ ( z ) = ( φ 1 ( z ) , ⋯ , φ l ( z ) ) \Phi (z)=( \varphi _1(z),\cdots ,\varphi _l(z)) be holomorphic from the unit ball of C n \mathbb C^n into the unit ball of C l \mathbb C^l . We denote by B α ( z , w ) B_{\alpha }(z,w) the weighted Bergman kernel. We give a condition for the kernel ( 1 − Φ ( z ) Φ ( w ) ¯ ) B α ( z , w ) (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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