Regularity properties of commutators and BMO-Triebel-Lizorkin spaces
Annales de l'Institut Fourier, Volume 45 (1995) no. 3, pp. 795-807.

In this paper we consider the regularity problem for the commutators ([b,R k ]) 1kn where b is a locally integrable function and (R j ) 1jn are the Riesz transforms in the n-dimensional euclidean space n . More precisely, we prove that these commutators ([b,R k ]) 1kn are bounded from L p into the Besov space B ˙ p s,p for 1<p<+ and 0<s<1 if and only if b is in the BMO-Triebel-Lizorkin space F ˙ s,p . The reduction of our result to the case p=2 gives in particular that the commutators ([b,R k ]) 1kn are bounded form L 2 into the Sobolev space H ˙ s if and only if b is in the BMO-Sobolev space F ˙ s,2 .

Nous nous intéressons à la régularité des commutateurs ([b,R k ]) 1kn b est une fonction localement intégrable et (R j ) 1jn désignent les transformées de Riesz. Nous montrons que si 1<p<+ et 0<s<1, alors les commutateurs ([b,R k ]) 1kn sont continus de L p ( n ) dans l’espace de Besov B ˙ p s,p si et seulement si b appartient à l’espace BMO-Triebel-Lizorkin F ˙ s,p . En particulier, si p=2, les commutateurs ([b,R k ]) 1kn sont continus de L 2 ( n ) dans l’espace de Sobolev H ˙ s si et seulement si b appartient à l’espace BMO-Sobolev F ˙ s,2 .

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     author = {Youssfi, Abdellah},
     title = {Regularity properties of commutators and $BMO${-Triebel-Lizorkin} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {795--807},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {45},
     number = {3},
     year = {1995},
     doi = {10.5802/aif.1474},
     zbl = {0827.46030},
     mrnumber = {96k:47089},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1474/}
}
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Youssfi, Abdellah. Regularity properties of commutators and $BMO$-Triebel-Lizorkin spaces. Annales de l'Institut Fourier, Volume 45 (1995) no. 3, pp. 795-807. doi : 10.5802/aif.1474. https://aif.centre-mersenne.org/articles/10.5802/aif.1474/

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