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L2 estimates for the ∂ operator on Stein manifolds

Published online by Cambridge University Press:  01 July 2000

PATRICK W. DARKO
PATRICK W. DARKO
Affiliation:
Department of Mathematics and Computer Science, Lincoln University, PA 19352, U.S.A.; e-mail: pdarko@lu.lincoln.edu
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Abstract

L2 estimates of the Kohn–Hörmander type are obtained for the ∂u operator on relatively compact Stein subdomains of complex manifolds. This is done by using a result of Hörmander locally, patching with cohomology of coherent analytic sheaves with bounds to get global solutions of the ∂u equation and then finishing with standard Hilbert space methods to obtain weak elliptic estimates.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 1 , July 2000 , pp. 73 - 76
Copyright
2000 Cambridge Philosophical Society

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