Compact operators on the Bergman space of multiply-connected domains

Raimondo, Roberto

doi:10.1090/S0002-9939-00-05718-X

Compact operators on the Bergman space of multiply-connected domains
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by Roberto Raimondo

Proc. Amer. Math. Soc. 129 (2001), 739-747

DOI: https://doi.org/10.1090/S0002-9939-00-05718-X

Published electronically: September 19, 2000

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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.

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