Inserted: 14 jun 2012
Last Updated: 18 jun 2015
Journal: Rev. Mat. Iberoam.
We prove some regularity estimates for a class of convex functions in Carnot-Carathéodory spaces, generated by Hörmander vector fields. Our approach relies on both the structure of metric balls induced by Hörmander vector fields and upper estimates for subsolutions of sub-Laplacians.
Keywords: convexity, Carnot-Carathéodory spaces, Lipschitz estimates, Hörmander condition