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Compact operators on the Bergman space of multiply-connected domains
Authors:Roberto Raimondo
Institution:Department of Economics, University of California at Berkeley, Evans Hall, Berkeley, California 94720
Abstract:

If $\Omega $ is a smoothly bounded multiply-connected domain in the complex plane and $A=\sum_{j=1}^m\prod_{k=1}^{m_j}T_{\varphi _{j,k}},$where $\varphi _{j,k}\in L^\infty ({\Omega },d{\nu }),$we show that $A$ is compact if and only if its Berezin transform vanishes at the boundary.

Keywords:
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