THE DISTRIBUTIONAL DIVERGENCE OF HORIZONTAL VECTOR FIELDS VANISHING AT INFINITY ON CARNOT GROUPS

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 & phi;, vanishing at infinity, that solves the equation divH & phi; = 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.