Quanhua Xu

Xiao Xiong

Zhi Yin

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.

Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori

Philippe Biane

Norio Konno

Fabio Cipriani

Luc Bouten

This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Quanhua Xu

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