Abstract: | This paper reveals that the sub-Laplacian L0 on two step stratified Lie groups has a similar behavior like elliptic operators on the Euclidean space, that is, the sub - Laplacian satisfies a group-elliptic estimate, called the G- elliptic estimate (or the Lp regularity), and the general left Invariant operator Lλ has such a behavior if and only if λ is admissible. |