In this paper, we prove the boundedness and compactness properties of the Bochner-Riesz commutator associated with the sub-Laplacians on Metivier groups. We show that the smoothness parameter can be expressed in terms of the topological dimension, rather than the homogeneous dimension of the Metivier groups. One of the main novel aspects of our proof is the use of weighted Plancherel estimates and truncated restriction-type estimates to obtain the threshold in terms of the topological dimension.

The first author was supported from his NBHM post-doctoral fellowship, DAE, Government of India. The second author would like to acknowledge the support of the Prime Minister's Research Fellows (PMRF) supported by Ministry of Education, Government of India.