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arXiv · 2202.11901

On the boundedness of multilinear Fourier multipliers on Hardy spaces

Jin Bong Lee·Bae Jun Park
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Abstract

In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier operator of H\"ormander type is bounded from $H^{p_1} \times \cdots \times H^{p_m}$ to $H^p$ for $0<p_1,\dots,p_m\le 1$ with $1/p_1 + \cdots 1/p_m = 1/p$, under suitable cancellation conditions. As a result, we extend the trilinear estimates of the authors(arXiv:2107.00225) to general multilinear ones and improve the boundedness result of the authors, Lee, Heo, Hong, Park, and Yang(Math. Ann. 381 : 499-555, 2021) in limiting situations.

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Jin Bong Lee, Bae Jun Park. 2022-02-24. On the boundedness of multilinear Fourier multipliers on Hardy spaces. https://arxiv.org/abs/2202.11901

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