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- W2962875380 abstract "We provide a study of the Riesz transforms on stratified nilpotent Lie groups, and obtain a certain version of the pointwise lower bound of the Riesz transform kernel. Then we establish the characterisation of the BMO space on stratified nilpotent Lie groups via the boundedness of the commutator of the Riesz transforms and the BMO function. This extends the well-known Coifman, Rochberg, Weiss theorem from Euclidean space to the setting of stratified nilpotent Lie groups. In particular, these results apply to the well-known example of the Heisenberg group. As an application, we also study the curl operator on the Heisenberg group and stratified nilpotent Lie groups, and establish the div–curl lemma with respect to the Hardy space on stratified nilpotent Lie groups. Nous étudions les transformées de Riesz sur les groupes de Lie nilpotents stratifiés, et obtenons une version d'estimée inférieure ponctuelle pour leur noyau. Nous donnons ensuite une caractérisation de l'espace BMO sur les groupes de Lie nilpotents stratifiés via la continuité du commutateur des transformées de Riesz avec une fonction BMO. Ceci étend le théorème connu de Coifman–Rochberg–Weiss de l'espace euclidien au cas des groupes de Lie nilpotents stratifiés. En particulier, ces résultats s'appliquent à l'exemple bien connu du groupe de Heisenberg. En tant qu'application, nous étudions également l'opérateur curl sur le groupe de Heisenberg et sur les groupes de Lie nilpotents stratifiés, et établissons le lemme div–curl sur l'espace de Hardy des groupes de Lie nilpotents stratifiés." @default.
- W2962875380 created "2019-07-30" @default.
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- W2962875380 date "2019-04-01" @default.
- W2962875380 modified "2023-10-12" @default.
- W2962875380 title "Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups" @default.
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- W2962875380 doi "https://doi.org/10.1016/j.matpur.2018.06.012" @default.
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