Calder\'on's commutator on Stratified Lie groups

Abstract

Motivated by the recent work of Gimperlein and Goffeng on Calder\'on's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's commutator on stratified Lie groups. We further study the related weak Schatten class estimates on two step stratified Lie groups, which include the Heisenberg groups