The G-Ellipticity for the Sub-Laplacian on Two Step Stratified Lie Groups

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 L^p regularity), and the general left Invariant operator L_λ has such a behavior if and only if λ is admissible.