Q-pseudoconvex and q-holomorphically convex domains

Abstract

In this article we prove a global result in the spirit of Basener's theorem regarding the relation between q-pseudoconvexity and q-holomorphic convexity: we prove that any smoothly bounded strictly q-pseudoconvex open subset of the complex Euclidean space is (q + 1)-holomorphically convex; moreover, assuming that the given open set verifies an additional assumption, we prove that it is q-holomorphically convex. We also prove that any open subset of the complex n-dimensional Euclidean space is n-holomorphically convex.