Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori (Memoirs of the American Mathematical Society)

Xiong, Xiao/ Xu, Quanhua/ Yin, Zhi

American Mathematical Society（2018/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 116 p.
• 言語 ENG
• 商品コード 9781470428068
• DDC分類 515.782

Full Description

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.

Contents

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