On some bilinear Fourier multipliers with oscillating factors, I
| Autor: | Kato, Tomoya, Miyachi, Akihiko, Shida, Naoto, Tomita, Naohito |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Bilinear Fourier multipliers of the form $e^{i (|\xi| + |\eta|+ |\xi + \eta|)} \sigma (\xi, \eta)$ are considered. It is proved that if $\sigma (\xi, \eta)$ is in the H\"ormander class $S^{m}_{1,0} (\mathbb{R}^{2n})$ with $m=-(n+1)/2$ then the corresponding bilinear operator is bounded in $L^{\infty} \times L^{\infty} \to bmo$, $h^{1} \times L^{\infty} \to L^{1}$, and $L^{\infty} \times h^{1} \to L^{1}$. This improves a result given by Rodr\'iguez-L\'opez, Rule and Staubach. Comment: 24 pages |
| Databáze: | arXiv |
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