Note on the Fenchel transform in the Heisenberg group
arXiv:0812.2753
Abstract
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.
The paper appeared in Journal of Mathematical Analysis and Applications, volume 368, issue 1, August 2010, pages 69-79.