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The Bergman projection and weighted $ C^k$ estimates for the canonical solution to the $ \bar{\partial}$ problem on non-smooth domains

Author: Dariush Ehsani
Journal: Trans. Amer. Math. Soc. 363 (2011), 3959-3975
MSC (2010): Primary 32A25, 32W05
Published electronically: March 10, 2011
MathSciNet review: 2792975
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Abstract | References | Similar Articles | Additional Information

Abstract: We apply integral representations for functions on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted $ C^k$-estimates for the component of a given function, $ f$, which is orthogonal to holomorphic functions in terms of $ C^k$-norms of $ \bar{\partial} f$. The weights are powers of the gradient of the defining function of the domain.

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Additional Information

Dariush Ehsani
Affiliation: Institut für Mathematik, Humboldt-Universität, 10099 Berlin, Germany

Received by editor(s): March 15, 2009
Published electronically: March 10, 2011
Additional Notes: This reasearch was partially supported by the Alexander von Humboldt Stiftung
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.