A local Martinelli-Bochner formula on hypersurfaces
Let \(M\) be a real \(C^ 2\) hypersurface in \(\mathbb{C}^ n\) whose Levi form has at least one positive and at least one negative eigenvalue at some point \(z_ 0 \in M\) (in tangential direction). We prove: There exist a neighborhood \(U \subseteq M\) of \(z_ 0\) and a continuous differential form \(K(z,y)\) defined for \(z,y \in U\) with \(z \neq y\), of bidegree \((n,n- 2)\) in \(y\) and of bidegree zero in \(z\), which has some useful properties with respect to Cauchy-Riemann functions on \(M\), similar to the properties of the Martinelli-Bochner kernel with respect to holomorphic functions.
real \(C^ 2\) hypersurface in \(\mathbb{C}^ n\)
scientific article; zbMATH DE number 567433
scientific article