Journal of Operator Theory

Volume 94, Issue 1, Summer 2025 pp. 151-174.

Calderon's commutator on stratified Lie groups

Authors: Yanping Chen (1), Zhenbing Gong (2), Ji Li (3), Edward McDonald (4), Dmitriy Zanin (5)
Author institution: (1) Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
(2) Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
(3) Department of Mathematics, Macquarie University, NSW 2109, Australia
(4) Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.
(5) School of Mathematics and Statistics, UNSW, Kensington, NSW 2052, Australia

Summary: 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 $L^p$ 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.

DOI: http://dx.doi.org/10.7900/jot.
Keywords: Calderon's commutator, stratified Lie groups, weak Schatten class

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