Uniform boundedness and compactness for the commutator of an extension of Riesz transform on stratified Lie groups - Han, Xueting; Chen, Yanping (Advances in nonlinear analysis, 2025)
Let be a stratified Lie group, and let be a basis of the left-invariant vector fields of degree one on and be the sub-Laplacian of . Given that , this article studies the commutators of order and establishes their uniform two-weight boundedness from to for any and via space, assuming that and . Based on this, we also give the characterization of space with respect to the uniform weighted compactness of for . As a consequence of our results, the corresponding boundedness and compactness for commutators of Riesz transforms on can be recovered as