Calderon's commutator on stratified Lie groups

Motivated by the recent work of Gimperlein and Goffeng on Calderon's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of Lp boundedness for Calderon's commutator on stratified Lie groups. We further study related weak Schatten class estimates for second order commutators on two step stratified Lie groups, which include the Heisenberg groups. This latter result is obtained using double operator integral techniques which are novel in this area.