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.
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Valentino Magnani, Matteo Scienza, Regularity estimates for convex functions in Carnot–Carathéodory spaces. Rev. Mat. Iberoam. 32 (2016), no. 3, pp. 835–858DOI 10.4171/RMI/900