Heisenberg型群上的仿积算子

宋乃琪, 赵纪满

数学学报 ›› 2016, Vol. 59 ›› Issue (4) : 433-450.

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数学学报 ›› 2016, Vol. 59 ›› Issue (4) : 433-450. DOI: 10.12386/A2016sxxb0042
论文

Heisenberg型群上的仿积算子

    宋乃琪1,2, 赵纪满2
作者信息 +

Paraproducts on Heisenberg Type Groups

    Nai Qi SONG1,2, Ji Man ZHAO2
Author information +
文章历史 +

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L2L2有界性.其次探讨了Heisenberg型群上的Calderón-Zygmund算子,包括该算子的LpLp有界性, L1L1,∞有界性以及H1L1有界性.最后证明了仿积算子也是Calderón-Zygmund算子,同时还证明了仿积算子的一些其它重要性质.

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.

关键词

Heisenberg型群 / 仿积 / Calderó / n-Zygmund算子

Key words

Heisenberg-type groups / paraproducts / Calderón-Zygmund operators

引用本文

导出引用
宋乃琪, 赵纪满. Heisenberg型群上的仿积算子. 数学学报, 2016, 59(4): 433-450 https://doi.org/10.12386/A2016sxxb0042
Nai Qi SONG, Ji Man ZHAO. Paraproducts on Heisenberg Type Groups. Acta Mathematica Sinica, Chinese Series, 2016, 59(4): 433-450 https://doi.org/10.12386/A2016sxxb0042

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基金

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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