Weighted $L^p$-Liouville theorems for hypoelliptic partial differential operators on Lie groups

We prove weighted Lp-Liouville theorems for a class of second order hypoelliptic partial differential operators L  on Lie groups whose underlying manifold is n-dimensional space. We show that a natural weight is the right-invariant measure Hˇ of . We also prove Liouville-type theorems for C2 subsolutions in Lp(,Hˇ). We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator L−∂t.