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Bilinear Spectral Multipliers on Heisenberg Groups

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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 \({{\cal C}_0}\left({{\mathbb{H}^n}} \right) \times {L^2}\left({{\mathbb{H}^n}} \right)\;{\rm{to}}\;{L^2}\left({{\mathbb{H}^n}} \right)\), from \({L^2}\left({{\mathbb{H}^n}} \right) \times {{\cal C}_0}\left({{\mathbb{H}^n}} \right)\;{\rm{to}}\;{L^2}\left({{\mathbb{H}^n}} \right)\), and from Lp × Lq to Lr with 2 < p, q < ∞, 2 ≤ r ≤ ∞.

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Authors and Affiliations

  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

    Naiqi Song  (宋乃琪) & Jiman Zhao  (赵纪满)

  2. School of Chinese Medicine, Beijing University of Chinese Medicine, Beijing, 100029, China

    Naiqi Song  (宋乃琪)

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Heping Liu  (刘和平)

Authors
  1. Naiqi Song  (宋乃琪)
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  2. Heping Liu  (刘和平)
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  3. Jiman Zhao  (赵纪满)
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Correspondence to Jiman Zhao  (赵纪满).

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

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Song, N., Liu, H. & Zhao, J. Bilinear Spectral Multipliers on Heisenberg Groups. Acta Math Sci 41, 968–990 (2021). https://doi.org/10.1007/s10473-021-0321-z

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

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