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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Global regularity for $ \bar \partial $ on weakly pseudo-convex manifolds


Author: J. J. Kohn
Journal: Trans. Amer. Math. Soc. 181 (1973), 273-292
MSC: Primary 35N15; Secondary 32F15, 58G05
MathSciNet review: 0344703
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Abstract: Let $ M'$ be a complex manifold and let $ M \subset \subset M'$ be an open pseudo-convex submanifold with a smooth boundary which can be exhausted by strongly pseudo-convex submanifolds. The main result of this paper is the following: Given a $ \overline \partial $-closed $ (p,q)$-form $ \alpha $, which is $ {C^\infty }$ on $ \overline M $ and which is cohomologous to zero on $ M$ then for every $ m$ there exists a $ (p,q - 1)$-form $ {u_{(m)}}$ which is $ {C^m}$ on $ \overline M $ such that $ \overline \partial {u_{(m)}} = \alpha $.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0344703-4
PII: S 0002-9947(1973)0344703-4
Article copyright: © Copyright 1973 American Mathematical Society