BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

doi:10.1007/s10473-021-0321-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 968-990.doi: 10.1007/s10473-021-0321-z

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

宋乃琪^1,2, 刘和平³, 赵纪满¹

1. Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Institution of Mathematics and Mathematical Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
2. School of Chinese Medicine, Beijing University of Chinese Medicine, Beijing 100029, China;
3. School of Mathematical Sciences, Peking University, Beijing 100871, China

收稿日期:2020-04-18 修回日期:2020-07-16 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Jiman ZHAO E-mail:jzhao@bnu.edu.cn
作者简介:Naiqi SONG,E-mail:songnaiqi2007@126.com;Heping LIU,E-mail:hpliu@math.pku.edu.cn
基金资助:
Supported by National Natural Science Foundation of China (11471040 and 11761131002).

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

Naiqi SONG^1,2, Heping LIU³, Jiman ZHAO¹

1. Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Institution of Mathematics and Mathematical Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
2. School of Chinese Medicine, Beijing University of Chinese Medicine, Beijing 100029, China;
3. School of Mathematical Sciences, Peking University, Beijing 100871, China

Received:2020-04-18 Revised:2020-07-16 Online:2021-06-25 Published:2021-06-07
Contact: Jiman ZHAO E-mail:jzhao@bnu.edu.cn
About author:Naiqi SONG,E-mail:songnaiqi2007@126.com;Heping LIU,E-mail:hpliu@math.pku.edu.cn
Supported by:
Supported by National Natural Science Foundation of China (11471040 and 11761131002).

摘要/Abstract

摘要： As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from $\mathcal{C}_{0}(\mathbb{H}^{n})\times L^{2}(\mathbb{H}^{n})$ to $L^{2}(\mathbb{H}^{n})$, from $ L^{2}(\mathbb{H}^{n}) \times \mathcal{C}_{0}(\mathbb{H}^{n})$ to $L^{2}(\mathbb{H}^{n})$, and from $L^{p}\times L^{q}$ to $L^{r}$ with $2 < p,q < \infty, 2\leq r \leq \infty$.

关键词: Bilinear spectral multipliers, Heisenberg groups, boundedness

Abstract: As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from $\mathcal{C}_{0}(\mathbb{H}^{n})\times L^{2}(\mathbb{H}^{n})$ to $L^{2}(\mathbb{H}^{n})$, from $ L^{2}(\mathbb{H}^{n}) \times \mathcal{C}_{0}(\mathbb{H}^{n})$ to $L^{2}(\mathbb{H}^{n})$, and from $L^{p}\times L^{q}$ to $L^{r}$ with $2 < p,q < \infty, 2\leq r \leq \infty$.

Key words: Bilinear spectral multipliers, Heisenberg groups, boundedness

中图分类号:

42B15

宋乃琪, 刘和平, 赵纪满. BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS[J]. 数学物理学报(英文版), 2021, 41(3): 968-990.

Naiqi SONG, Heping LIU, Jiman ZHAO. BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS[J]. Acta mathematica scientia,Series B, 2021, 41(3): 968-990.

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BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

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