The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups

  • A. Baldi University of Bologna, Italy
  • F. Montefalcone University of Padova, Italy


We define a BV-type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributions F for which there exists a continuous horizontal vector field Φ, vanishing at infinity, that solves the equation divHΦ = F . This generalizes to the setting of Carnot groups some results by De Pauw and Pfeffer, [13], and by De Pauw and Torres, [14], for the Euclidean setting.