DOI: 10.68381/jca15050 ISSN: 0944-6532
On Weakly H-Quasiconvex Functions on the Heisenberg Group
Andrea Calogero, Giovanna Carcano, Rita Pini
The aim of this paper is the investigation of weakly H-quasiconvex functions in the framework of the Heisenberg group
\mathbb{H}
H
. The functions of this class, recently introduced by M. B. Sun and X. P. Yang ["Some properties of quasiconvex functions on the Heisenberg Group", Acta Math. Appl. Sinica 21 (2005) 571–580], are defined via the property that their sublevels are weakly H-convex subsets of
\mathbb{H}
H
. Following Crouzeix's approach, we prove conditions of first and second order, easily testable, for regular weakly H-quasiconvex functions, and we provide a characterization of them.