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q ‐pseudoconvex and q ‐holomorphically convex domains
Author(s) -
Ioniţă GeorgeIonuţ,
Preda Ovidiu
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800259
Subject(s) - mathematics , holomorphic function , pseudoconvex function , convexity , regular polygon , pure mathematics , boundary (topology) , subderivative , mathematical analysis , convex optimization , geometry , economics , financial economics
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 open subset Ω ⊂ C nwith smooth boundary, strictly q ‐pseudoconvex, is ( q + 1 ) ‐holomorphically convex; moreover, assuming that Ω verifies an additional assumption, we prove that it is q ‐holomorphically convex. We also prove that any open subset of C n is n ‐holomorphically convex.