Download or read book Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori written by Xiao Xiong and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -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 Poincaré type inequality for Sobolev spaces.