Lorentz boundedness and compactness of Riesz transform commutator on stratified Lie groups

The Lp boundedness of the commutator [b, T] has been intensively studied in recent decades in part because it has important connections and applications to partial differential equations. Inspired by these works, we study the boundedness and compactness of the Riesz transform commutator in a general setting, namely in the scale of Lorentz spaces and on stratified Lie groups. In this paper we provide a complete characterization between the space of the symbol b and the Lorentz estimates of [b,Rj ].