Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori

English | 2018 | ISBN: 1470428067 | 130 Pages | PDF | 1.17 MB


English | 2018 | ISBN: 1470428067 | 130 Pages | PDF | 1.17 MB
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative d-torus T d\theta (with \theta a skew symmetric real d x 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.

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