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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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
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by Dariush Ehsani PDF
Trans. Amer. Math. Soc. 363 (2011), 3959-3975 Request permission

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
  • Email: dehsani.math@gmail.com
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3959-3975
  • MSC (2010): Primary 32A25, 32W05
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05277-3
  • MathSciNet review: 2792975