Harmonic Analysis on Quantum Tori
文献类型：期刊论文
| 作者 | Chen, Zeqian1; Xu, Quanhua2,3; Yin, Zhi2,3 |
| 刊名 | COMMUNICATIONS IN MATHEMATICAL PHYSICS
 |
| 出版日期 | 2013-09-01 |
| 卷号 | 322期号:3页码:755-805 |
| 英文摘要 | This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fej,r means, square and circular Poisson means, and Bochner-Riesz means. We first establish the maximal inequalities for these means, then obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. The second part of the paper deals with Fourier multipliers on quantum tori. We prove that the completely bounded L (p) Fourier multipliers on a quantum torus are exactly those on the classical torus of the same dimension. Finally, we present the Littlewood-Paley theory associated with the circular Poisson semigroup on quantum tori. We show that the Hardy spaces in this setting possess the usual properties of Hardy spaces, as one can expect. These include the quantum torus analogue of Fefferman's H-1-BMO duality theorem and interpolation theorems. Our analysis is based on the recent developments of noncommutative martingale/ergodic inequalities and Littlewood-Paley-Stein theory. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Physics, Mathematical |
| 研究领域[WOS] | Physics |
| 关键词[WOS] | NONCOMMUTATIVE BURKHOLDER/ROSENTHAL INEQUALITIES ; MAXIMAL ERGODIC-THEOREMS ; MARTINGALES ; SPACES ; ALGEBRAS ; LOCALIZATION ; TRANSFORMS |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000321957000004 |
| 公开日期 | 2015-07-14 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/846]  |
| 专题 | 武汉物理与数学研究所_数学物理与应用研究部 |
| 作者单位 | 1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 2.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China 3.Univ Franche Comte, Math Lab, F-25030 Besancon, France |
| 推荐引用方式 GB/T 7714 | Chen, Zeqian,Xu, Quanhua,Yin, Zhi. Harmonic Analysis on Quantum Tori[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2013,322(3):755-805. |
| APA | Chen, Zeqian,Xu, Quanhua,&Yin, Zhi.(2013).Harmonic Analysis on Quantum Tori.COMMUNICATIONS IN MATHEMATICAL PHYSICS,322(3),755-805. |
| MLA | Chen, Zeqian,et al."Harmonic Analysis on Quantum Tori".COMMUNICATIONS IN MATHEMATICAL PHYSICS 322.3(2013):755-805. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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