Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 968-990.doi: 10.1007/s10473-021-0321-z

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Naiqi SONG1,2, Heping LIU3, Jiman ZHAO1   

  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
  • Received:2020-04-18 Revised:2020-07-16 Online:2021-06-25 Published:2021-06-07
  • Contact: Jiman ZHAO
  • About author:Naiqi SONG,;Heping LIU,
  • Supported by:
    Supported by National Natural Science Foundation of China (11471040 and 11761131002).

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

CLC Number: 

  • 42B15