This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $\mathbb{T}^d_\theta$ (with $\theta$ a skew symmetric real $d\times d$-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.
| ISBN: | 9781470428068 |
| Publication date: | 30th April 2018 |
| Author: | Xiao Xiong, Quanhua Xu, Zhi Yin |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 118 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Calculus and mathematical analysis |