Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori

ISBN-13: 9781470428068 / Angielski

Xiao Xiong;Quanhua Xu;Zhi Yin

Opis

This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative $d$-torus $mathbb^d_ heta$ (with $ heta$ a skew symmetric real $d imes d$-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.

Spis treści

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