L2 estimates for the ∂ operator on Stein manifolds

L2 estimates for the ∂ operator on Stein manifolds

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...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2000-07, Vol.129 (1), p.73-76
1. Verfasser: DARKO, PATRICK W.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100004436