BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

Naiqi SONG; Heping LIU; Jiman ZHAO

doi:10.1007/s10473-021-0321-z

Acta mathematica scientia, Series B >

2021 , Vol. 41 >Issue 3: 968 - 990

DOI: https://doi.org/10.1007/s10473-021-0321-z

Articles

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

Naiqi SONG ,
Heping LIU ,
Jiman ZHAO

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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

Naiqi SONG,E-mail:songnaiqi2007@126.com;Heping LIU,E-mail:hpliu@math.pku.edu.cn

Received date: 2020-04-18

Revised date: 2020-07-16

Online published: 2021-06-07

Supported by

Supported by National Natural Science Foundation of China (11471040 and 11761131002).

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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

Cite this article

Naiqi SONG , Heping LIU , Jiman ZHAO . BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS[J]. Acta mathematica scientia, Series B, 2021 , 41(3) : 968 -990 . DOI: 10.1007/s10473-021-0321-z

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