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June 1979 Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn
Steven G. Krantz
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Illinois J. Math. 23(2): 267-285 (June 1979). DOI: 10.1215/ijm/1256048239

Abstract

It is shown that the only pseudoconvex sets with smooth boundary in $\mathbf{C}^{n}$ on which $\bar{\partial}$ satisfies Lipschitz smoothing estimates of order $1/2$ are the strongly pseudoconvex ones. Various extensions of this result are made to weakly pseudoconvex domains of finite type and in various norms. It is proved that subelliptic estimates for $\bar{\partial}$ can hold on a pseudoconvex set in $\mathbf{C}^{n}$ only if the domain is of finite type in the sense of Kohn.

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Steven G. Krantz. "Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn." Illinois J. Math. 23 (2) 267 - 285, June 1979. https://doi.org/10.1215/ijm/1256048239

Information

Published: June 1979
First available in Project Euclid: 20 October 2009

zbMATH: 0394.32009
MathSciNet: MR528563
Digital Object Identifier: 10.1215/ijm/1256048239

Subjects:
Primary: 32F15
Secondary: 32F20

Rights: Copyright © 1979 University of Illinois at Urbana-Champaign

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Vol.23 • No. 2 • June 1979
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