Abstract
In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of Hörmander type is bounded from \({H^{{p_1}}} \times \cdots \times {H^{{p_m}}}\) to Hp for 0 < p1, …, pm ≤ 1 with 1/p1+ ⋯ + 1/pm = 1/p, under suitable cancellation conditions. As a result, we extend the trilinear estimates in [17] to general multilinear ones and improve the boundedness result in [18] in limiting situations.
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We would like to thank the anonymous referees for the careful reading and their helpful comments.
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J. B. Lee is supported by NRF grant 2021R1C1C2008252.
B. Park is supported in part by NRF grant 2022R1F1A1063637 and was supported in part by a KIAS Individual Grant MG070001 at the Korea Institute for Advanced Study.
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Lee, J.B., Park, B.J. On the boundedness of multilinear Fourier multipliers on Hardy spaces. JAMA 150, 275–301 (2023). https://doi.org/10.1007/s11854-022-0268-6
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DOI: https://doi.org/10.1007/s11854-022-0268-6