Uniform boundedness and compactness for the commutator of an extension of Riesz transform on stratified Lie groups

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 . Base...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 14; no. 1; pp. 1207 - 1230
Main Authors Han, Xueting, Chen, Yanping
Format Journal Article
LanguageEnglish
Published De Gruyter 04.07.2025
Subjects
22E30
42B20
42B35
43A15
BMO space
Riesz transform
stratified Lie groups
VMO space
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Summary: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
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2025-0092