Nous nous intéressons à la régularité des commutateurs où est une fonction localement intégrable et désignent les transformées de Riesz. Nous montrons que si et , alors les commutateurs sont continus de dans l’espace de Besov si et seulement si appartient à l’espace -Triebel-Lizorkin . En particulier, si , les commutateurs sont continus de dans l’espace de Sobolev si et seulement si appartient à l’espace -Sobolev .
In this paper we consider the regularity problem for the commutators where is a locally integrable function and are the Riesz transforms in the -dimensional euclidean space . More precisely, we prove that these commutators are bounded from into the Besov space for and if and only if is in the -Triebel-Lizorkin space . The reduction of our result to the case gives in particular that the commutators are bounded form into the Sobolev space if and only if is in the -Sobolev space .
@article{AIF_1995__45_3_795_0, author = {Youssfi, Abdellah}, title = {Regularity properties of commutators and $BMO$-Triebel-Lizorkin spaces}, journal = {Annales de l'Institut Fourier}, volume = {45}, year = {1995}, pages = {795-807}, doi = {10.5802/aif.1474}, mrnumber = {96k:47089}, zbl = {0827.46030}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1995__45_3_795_0} }
Youssfi, Abdellah. Regularity properties of commutators and $BMO$-Triebel-Lizorkin spaces. Annales de l'Institut Fourier, Tome 45 (1995) pp. 795-807. doi : 10.5802/aif.1474. http://gdmltest.u-ga.fr/item/AIF_1995__45_3_795_0/
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