The
\bar \partial
-Neumann operator and commutators of the Bergman projection and multiplication operators |
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Authors: | Friedrich Haslinger |
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Institution: | 1. Institut für Mathematik, Universit?t Wien, Nordbergstra?e 15, A-1090, Wien, Austria
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Abstract: | We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. |
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Keywords: | ![](/content/g451675k542572q6/10587_2008_84_Article_IEq8) gif" alt="$$
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-equation" target="_blank">$$" align="middle" border="0">-equation ![](/content/g451675k542572q6/10587_2008_84_Article_IEq9) gif" alt="$$
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