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\(H^p\) Boundedness of Multilinear Spectral Multipliers on Stratified Groups

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Abstract

As far as we know, there is no study about \(H^p\) boundedness of multilinear spectral multipliers on nilpotent Lie groups. In this paper, on stratified groups G, we prove a Hörmander type multiplier theorem for multilinear spectral multipliers on Hardy spaces, i.e., the boundedness from \(H^{p_1}\times H^{p_2} \times \cdots \times H^{p_N}\) to \(L^p\) with \(0<p_1,\ldots ,p_N,p \leqslant \infty \).

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Acknowledgements

The authors would like to express great gratitude to the referees for the valuable comments and helpful suggestions.

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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

    Jingxuan Fang & Jiman Zhao

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  1. Jingxuan Fang
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Jiman Zhao is the corresponding author and supported by National Natural Science Foundation of China (Grant Nos. 11471040 and 11761131002).

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Fang, J., Zhao, J. \(H^p\) Boundedness of Multilinear Spectral Multipliers on Stratified Groups. J Geom Anal 30, 197–222 (2020). https://doi.org/10.1007/s12220-018-00142-7

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