Revista Matemática Iberoamericana


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Volume 32, Issue 3, 2016, pp. 835–858
DOI: 10.4171/RMI/900

Published online: 2016-10-03

Regularity estimates for convex functions in Carnot–Carathéodory spaces

Valentino Magnani[1] and Matteo Scienza[2]

(1) Università di Pisa, Italy
(2) Università di Pisa, Italy

We prove some first order 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 local upper estimates for the corresponding subharmonic functions.

Keywords: Convexity, Hörmander condition, Carnot–Carathéodory spaces, Lipschitz estimates

Magnani Valentino, Scienza Matteo: Regularity estimates for convex functions in Carnot–Carathéodory spaces. Rev. Mat. Iberoamericana 32 (2016), 835-858. doi: 10.4171/RMI/900