Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori

Xiao Xiong, Quanhua Xu, Zhi Yin (Autoren)

Buch | Softcover

116 Seiten

2018
American Mathematical Society (Verlag)
978-1-4704-2806-8 (ISBN)

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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.

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.

Xiao Xiong, Wuhan University, China, and Universite de Franche-Comte, Besancon, France. Quanhua Xu, Wuhan University, China, and Universite de Franche-Comte, Besancon, France. Zhi Yin, Wuhan University, China.

Introduction
Preliminaries
Sobolev spaces
Besov spaces
Triebel-Lizorkin spaces
Interpolation
Embedding
Fourier multiplier
Bibliography

Erscheinungsdatum	07.01.2018
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	240 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2806-7 / 1470428067
ISBN-13	978-1-4704-2806-8 / 9781470428068
Zustand	Neuware