| Heisenberg型群上的仿积算子 |
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| 引用本文： | 宋乃琪,赵纪满.Heisenberg型群上的仿积算子[J].数学学报,2016,59(4):433-450. |
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| 作者姓名： | 宋乃琪 赵纪满 |
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| 作者单位： | 1. 北京中医药大学中药学院 北京 100029;
2. 北京师范大学数学科学学院数学与复杂系统教育部重点实验室 北京 100875 |
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| 基金项目： | 国家自然科学基金资助项目(11471040);中央高校基本科研业务费专项资金(2014KJJCA10) |
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| 摘 要： | 首先给出了Heisenberg型群上一类仿积算子的定义,研究了该算子的L~2→L~2有界性.其次探讨了Heisenberg型群上的Calderon-Zygmund算子,包括该算子的L~p→L~p有界性,L~1→L~(1,∞)有界性以及H~1→L~1有界性.最后证明了仿积算子也是Calderon-Zygmund算子,同时还证明了仿积算子的一些其它重要性质.
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| 关 键 词： | Heisenberg型群 仿积 Calderón-Zygmund算子 |
Paraproducts on Heisenberg Type Groups |
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| Nai Qi SONG,Ji Man ZHAO.Paraproducts on Heisenberg Type Groups[J].Acta Mathematica Sinica,2016,59(4):433-450. |
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| Authors: | Nai Qi SONG Ji Man ZHAO |
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| Institution: | 1. Beijing University of Chinese Medicine, Beijing 100029, P. R. China;
2. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | We define a class of paraproducts on Heisenberg type groups. We prove they have L2 boundedness. We also study Calderón-Zygmund operators, and prove they are bounded operators which map Lp to Lp, L1 to L1,∞ and H1 to L1. Then we prove the paraproducts are also Calderón-Zygmund operators and they also satisfy two important properties that Pb1=b and Pbt(1)=0 in the sense of distribution. |
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| Keywords: | Heisenberg-type groups paraproducts Calderón-Zygmund operators |
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