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Title: The $\bar\partial$-Neumann operator and commutators of the Bergman projection and multiplication operators (English)
Author: Haslinger, Friedrich
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 4
Year: 2008
Pages: 1247-1256
Summary lang: English
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Category: math
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Summary: We prove that compactness of the canonical solution operator to $\bar \partial $ restricted to $(0,1)$-forms with holomorphic coefficients is equivalent to compactness of the commutator $[\mathcal P,\bar M]$ defined on the whole $L^2_{(0,1)}(\Omega ),$ where $\bar M$ is the multiplication by $\bar z$ and $\mathcal P $ is the orthogonal projection of $L^2_{(0,1)}(\Omega )$ to the subspace of $(0,1)$ forms with holomorphic coefficients. Further we derive a formula for the $\bar \partial $-Neumann operator restricted to $(0,1)$ forms with holomorphic coefficients expressed by commutators of the Bergman projection and the multiplications operators by $z $ and $\bar z$. (English)
Keyword: $\bar{\partial}$-equation
Keyword: $\bar{\partial}$-Neumann operator
Keyword: compactness
MSC: 32A36
MSC: 32W05
idZBL: Zbl 1174.32015
idMR: MR2471181
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Date available: 2010-07-21T08:18:02Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/140455
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