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<p>In this paper, on Heisenberg group, we consider a spectral multiplier theorem on Hardy spaces <i>H</i><sup><i>p</i></sup>. By replacing the usual Sobolev space <i>L</i><Stack> <sub><i>s</i></sub> <sup>2</sup> </Stack> by the locally largest Lorentz-Sobolev space <i>L</i><Stack> <sub><i>s</i></sub> <sup><i>p,q</i></sup> </Stack>, we make an estimate of the kernel function of spectral multipliers with a Lorentz-Sobolev norm. Then we prove a Hörmander type multiplier theorem for spectral multiplier on Hardy spaces <i>H</i><sup><i>p</i></sup> with 0 &lt; <i>p</i> ≤ ∞.</p>

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Hp boundedness of spectral multipliers on Heisenberg groups

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Nan Hu,
  • Jiman Zhao

摘要

In this paper, on Heisenberg group, we consider a spectral multiplier theorem on Hardy spaces Hp. By replacing the usual Sobolev space L s 2 by the locally largest Lorentz-Sobolev space L s p,q , we make an estimate of the kernel function of spectral multipliers with a Lorentz-Sobolev norm. Then we prove a Hörmander type multiplier theorem for spectral multiplier on Hardy spaces Hp with 0 < p ≤ ∞.