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Some applications of Cauchy-Fantappiè forms to (local) problems on \({\bar \partial}_ b\). (English) Zbl 0633.32007
A \({\bar \partial}_ b\)-closed smooth (0,q)-form g on some real hypersurface \(\Sigma \subset {\mathbb{C}}^ n\) is shown to be locally represented as the “jump” between two smooth \({\bar \partial}\)-closed forms. This fact allows one to establish that under some assumptions on \(\Sigma\) there exists a \((0,q-1)-\)form u on \(\Sigma\) verifying \({\bar \partial}_ bu=g\) for \(q=1,...,n-3\), and under additional hypothesis this is also true for \(q=n-2\). The techniques of vanishing Cauchy- Fantappiè kernels are used.
Reviewer: A.Yu.Rashkovskij

MSC:
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32V40 Real submanifolds in complex manifolds
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