On some bilinear Fourier multipliers with oscillating factors, I
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913618817187840 |
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| author | Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito |
| author_facet | Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito |
| contents | Bilinear Fourier multipliers of the form $e^{i (|ξ| + |η|+ |ξ+ η|)} σ(ξ, η)$ are considered. It is proved that if $σ(ξ, η)$ is in the Hörmander 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 Rodríguez-López, Rule and Staubach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14742 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some bilinear Fourier multipliers with oscillating factors, I Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito Classical Analysis and ODEs 42B15, 42B20 Bilinear Fourier multipliers of the form $e^{i (|ξ| + |η|+ |ξ+ η|)} σ(ξ, η)$ are considered. It is proved that if $σ(ξ, η)$ is in the Hörmander 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 Rodríguez-López, Rule and Staubach. |
| title | On some bilinear Fourier multipliers with oscillating factors, I |
| topic | Classical Analysis and ODEs 42B15, 42B20 |
| url | https://arxiv.org/abs/2412.14742 |