Comptes Rendus
Functional analysis
Function spaces on quantum tori
Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 729-734.

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 (Lp(Tθd),Wpk(Tθd)); descriptions of completely bounded Fourier multipliers on these spaces.

On considère les espaces de Sobolev, Besov et Triebel–Lizorkin sur un tore quantique Tθd 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 (Lp(Tθd),Wpk(Tθd)) ; l'indépendance en θ des multiplicateurs de Fourier complètement bornés sur ces espaces.

Published online:
DOI: 10.1016/j.crma.2015.06.002

Xiao Xiong 1; Quanhua Xu 1, 2; Zhi Yin 2

1 Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon cedex, France
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
     author = {Xiao Xiong and Quanhua Xu and Zhi Yin},
     title = {Function spaces on quantum tori},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {729--734},
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     year = {2015},
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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.

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