Laurent-Thiébaut, Christine Transformation de Bochner-Martinelli dans une variété de Stein. (A Bochner-Martinelli transform on Stein manifolds). (French) Zbl 0691.32003 Sémin. d’analyse P. Lelong - P. Dolbeault - H. Skoda, Paris 1985/86, Lect. Notes Math. 1295, 96-131 (1987). Summary: [For the entire collection see Zbl 0623.00006.] Let f be a \({\mathcal C}^ 1\) differential form or a current of order zero with compact support on a real hypersurface of a Stein manifold; using Henkin-Leiterer’s global kernels on a Stein manifold, we define a generalized Bochner-Martinelli transform of f and study its behaviour on the hypersurface. When the hypersurface is the boundary of a relatively compact domain and if f is a measure which verifies the Cauchy-Riemann conditions, we obtain a generalization of the Bochner extension theorem. Cited in 3 Documents MSC: 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32E10 Stein spaces 32H99 Holomorphic mappings and correspondences Keywords:Stein manifold; generalized Bochner-Martinelli transform Citations:Zbl 0623.00006 PDFBibTeX XML