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Comptes Rendus Mathématique
Volume 353, n° 8
pages 729-734 (août 2015)
Doi : 10.1016/j.crma.2015.06.002
Received : 11 May 2015 ;  accepted : 3 June 2015
Function spaces on quantum tori
Espaces de fonctions sur les tores quantiques
 

Xiao Xiong a , Quanhua Xu b, a , Zhi Yin b
a Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon cedex, France 
b School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

The full text of this article is available in PDF format.


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