2008/12/15 by Calogero, A., Pini, R.
#26B25 (Secondary) #52A01 (Primary) 53C17 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.0812.2753
Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the Euclidean case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role.