Calder\'on's commutator on Stratified Lie groups

TL;DR

This paper characterizes the boundedness of Calderón's commutator on stratified Lie groups and introduces novel double operator integral techniques for weak Schatten class estimates, extending previous work on Heisenberg groups.

Contribution

It provides the first characterization of $L^p$ boundedness for Calderón's commutator on stratified Lie groups and develops new methods for weak Schatten class estimates.

Findings

Established $L^p$ boundedness criteria for Calderón's commutator on stratified Lie groups.

Derived weak Schatten class estimates for second order commutators on two-step stratified Lie groups.

Introduced double operator integral techniques to this area of harmonic analysis.

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 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.