Hölder regularity of \(\overline{\partial_ b}\) in convex-concave hypersurfaces
Let \(M\) be a real hypersurface of class \(C^2\) in a complex analytic manifold. Suppose that the Levi form of \(M\) has at each point at least a pair of eigenvalues of opposite sign. In this paper we prove a regularity theorem for \(\overline {\partial}_b\) and a theorem of type Hartogs-Bochner on \(M\). Our key ingredient is a Hölder estimate for a local Martinelli-Bochner kernel constructed by \textit{B. Fischer} and \textit{J. Leiterer} on \(M\) [Math. Z. 214, No. 4, 659-681 (1993; Zbl 0791.32006)].
scientific article; zbMATH DE number 838482