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On the Friedrichs operator

Authors: Peng Lin and Richard Rochberg
Journal: Proc. Amer. Math. Soc. 123 (1995), 3335-3342
MSC: Primary 47B38; Secondary 32A37, 32H10, 46E99, 47B10
MathSciNet review: 1264822
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Abstract: Let $ \Omega $ be a simply connected domain in $ {\mathbb{C}^1}$ with the area measure dA. Let $ {\bar P_\Omega }$ be the orthogonal projection from $ {L^2}(\Omega ,dA)$ onto the closed subspace of antiholomorphic functions in $ {L^2}(\Omega ,dA)$. The Friedrichs operator $ {\bar T_\Omega }$ associated to $ \Omega $ is the operator from the Bergman space $ L_a^2(\Omega )$ into $ {L^2}(\Omega ,dA)$ defined by $ {\bar T_\Omega }f = {\bar P_\Omega }f$. In this note, some smoothness conditions on the boundary of $ \Omega $ are given such that the Friedrichs operator $ {\bar T_\Omega }$ belongs to the Schatten classes $ {S_p}$.

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Article copyright: © Copyright 1995 American Mathematical Society

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