Local Hardy and Rellich inequalities for sums of squares of vector   fields
  We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give some explicit examples, in particular, for sums of squares of vector fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups. 
Michael Ruzhansky and Durvudkhan Suragan
math.AP math.SP