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October 2004 The $\bar \partial $ -problem with support conditions on some weakly pseudoconvex domainswith support conditions on some weakly pseudoconvex domains
Judith Brinkschulte
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Ark. Mat. 42(2): 259-282 (October 2004). DOI: 10.1007/BF02385479

Abstract

We consider a domain Ω with Lipschitz boundary, which is relatively compact in an n-dimensional Kähler manifold and satisfies some “logδ-pseudoconvexity” condition. We show that the $\bar \partial $ -equation with exact support in ω admits a solution in bidegrees (p, q), 1≤qn−1. Moreover, the range of $\bar \partial $ acting on smooth (p, n−1)-forms with support in $\bar \Omega $ is closed. Applications are given to the solvability of the tangential Cauchy-Riemann equations for smooth forms and currents for all intermediate bidegrees on boundaries of weakly pseudoconvex domains in Stein manifolds and to the solvability of the tangential Cauchy-Riemann equations for currents on Levi flat CR manifolds of arbitrary codimension.

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Judith Brinkschulte. "The $\bar \partial $ -problem with support conditions on some weakly pseudoconvex domainswith support conditions on some weakly pseudoconvex domains." Ark. Mat. 42 (2) 259 - 282, October 2004. https://doi.org/10.1007/BF02385479

Information

Received: 12 December 2002; Revised: 25 July 2003; Published: October 2004
First available in Project Euclid: 31 January 2017

zbMATH: 1078.32023
MathSciNet: MR2101387
Digital Object Identifier: 10.1007/BF02385479

Rights: 2004 © Institut Mittag-Leffler

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Vol.42 • No. 2 • October 2004
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