We study Sobolev, Besov and Triebel–Lizorkin spaces on quantum tori. These spaces share many properties with their classical counterparts. The results announced include: Besov and Sobolev embedding theorems; Littlewood–Paley-type characterizations of Besov and Triebel–Lizorkin spaces; an explicit description of the K-functional of ; descriptions of completely bounded Fourier multipliers on these spaces.
On considère les espaces de Sobolev, Besov et Triebel–Lizorkin sur un tore quantique de d générateurs. Les principaux résultats comprennent : le plongement de Besov et Sobolev ; des caractérisations à la Littlewood–Paley pour les espaces de Besov et Triebel–Lizorkin ; une formule explicite de la K-fonctionnelle de ; l'indépendance en θ des multiplicateurs de Fourier complètement bornés sur ces espaces.
Accepted:
Published online:
Xiao Xiong 1; Quanhua Xu 1, 2; Zhi Yin 2
@article{CRMATH_2015__353_8_729_0, author = {Xiao Xiong and Quanhua Xu and Zhi Yin}, title = {Function spaces on quantum tori}, journal = {Comptes Rendus. Math\'ematique}, pages = {729--734}, publisher = {Elsevier}, volume = {353}, number = {8}, year = {2015}, doi = {10.1016/j.crma.2015.06.002}, language = {en}, }
Xiao Xiong; Quanhua Xu; Zhi Yin. Function spaces on quantum tori. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 729-734. doi : 10.1016/j.crma.2015.06.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.002/
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