Q-pseudoconvex and q-holomorphically convex domains

2018/09/03 by George‐Ionuţ Ioniţă, Ionita, George-Ionut, Ovidiu Preda +1
Mathematics · #32F10 #32F17 #32T40 #Advanced Banach Space Theory #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1809.00728

openalex publication_date 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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