JournalsrmiVol. 32, No. 3pp. 835–858

Regularity estimates for convex functions in Carnot–Carathéodory spaces

  • Valentino Magnani

    Università di Pisa, Italy
  • Matteo Scienza

    Università di Pisa, Italy
Regularity estimates for convex functions in Carnot–Carathéodory spaces cover
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Abstract

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.

Cite this article

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

DOI 10.4171/RMI/900