  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.
