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arXiv · 2306.08462

A sharp H\"{o}rmander estimate for multi-parameter and multi-linear Fourier multiplier operators

Jiao Chen·Danqing He·Guozhen Lu·Bae Jun Park·Lu Zhang
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Abstract

In this paper, we investigate the H\"ormander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by $L^u$-based Sobolev norms for $1<u\le 2$ , our results on the smoothness assumptions are sharp in the multi-parameter and bilinear case. In the multi-parameter and multi-linear case, our results are almost sharp. Moreover, even in the one-parameter and multi-linear case, our results improve earlier ones in the literature.

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Jiao Chen, Danqing He, Guozhen Lu, Bae Jun Park, Lu Zhang. 2023-06-14. A sharp H\"{o}rmander estimate for multi-parameter and multi-linear Fourier multiplier operators. https://arxiv.org/abs/2306.08462

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