Hypoellipticity, fundamental solution and Liouville type theorem for matrix-valued differential operators in Carnot groups

  • Bruno Franchi

    Università di Bologna, Italy
  • Annalisa Baldi

    Università di Bologna, Italy
  • Maria Carla Tesi

    Università di Bologna, Italy

Abstract

Let be a non-negative self-adjoint matrix-valued operator of order on a Carnot group . Here is the homogeneous dimension of . The aim of this paper is to investigate the relationship between hypoellipticity and maximal hypoellipticity (i.e. sharp estimates in appropriate Sobolev spaces), -maximal hypoellipticity (i.e. sharp estimates in appropriate Sobolev spaces for {}), and what we call maximal subellipticity of (which is basically a sharp higher order energy estimate).

Cite this article

Bruno Franchi, Annalisa Baldi, Maria Carla Tesi, Hypoellipticity, fundamental solution and Liouville type theorem for matrix-valued differential operators in Carnot groups. J. Eur. Math. Soc. 11 (2009), no. 4, pp. 777–798

DOI 10.4171/JEMS/166