On some bilinear Fourier multipliers with oscillating factors, II
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912171348197376 |
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| author | Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito |
| author_facet | Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito |
| contents | For $s > 0$, $s \neq 1$, bilinear Fourier multipliers of the form $e^{i (|ξ|^s + |η|^s+ |ξ+ η|^s)} σ(ξ, η)$ are considered, where $σ(ξ, η)$ belongs to the Hörmander class $S^{m}_{1, 0}(\mathbb{R}^{2n})$. A criterion for $m$ to ensure the $L^{\infty}\times L^{\infty} \to L^\infty$, $L^{1} \times L^{\infty} \to L^{1}$, and $L^{\infty} \times L^{1} \to L^{1}$ boundedness of the corresponding bilinear operators is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some bilinear Fourier multipliers with oscillating factors, II Kato, Tomoya Miyachi, Akihiko Shida, Naoto Tomita, Naohito Classical Analysis and ODEs 42B15, 42B20 For $s > 0$, $s \neq 1$, bilinear Fourier multipliers of the form $e^{i (|ξ|^s + |η|^s+ |ξ+ η|^s)} σ(ξ, η)$ are considered, where $σ(ξ, η)$ belongs to the Hörmander class $S^{m}_{1, 0}(\mathbb{R}^{2n})$. A criterion for $m$ to ensure the $L^{\infty}\times L^{\infty} \to L^\infty$, $L^{1} \times L^{\infty} \to L^{1}$, and $L^{\infty} \times L^{1} \to L^{1}$ boundedness of the corresponding bilinear operators is given. |
| title | On some bilinear Fourier multipliers with oscillating factors, II |
| topic | Classical Analysis and ODEs 42B15, 42B20 |
| url | https://arxiv.org/abs/2412.20010 |