A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators

In this paper, we investigate the Hörmander 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 ≤ 2 , our results on the smoothness assumptions are sharp in the multi-parameter and bilinear case....

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Bibliographic Details
Published in:Mathematische annalen 2024, Vol.390 (4), p.5923-5985
Main Authors: Chen, Jiao, He, Danqing, Lu, Guozhen, Park, Bae Jun, Zhang, Lu
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Multipliers
Parameter estimation
Smoothness
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Summary:In this paper, we investigate the Hörmander 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 ≤ 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-024-02893-x