This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $mathbb^d_ heta$ (with $ heta$ a skew symmetric real $d imes d$-matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincare type inequality for Sobolev spaces.
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $mathbb^d_ heta$ (with $ heta$ a sk...
