Fourier extension estimates on a strip in $\mathbb{R}^2$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914031109931008 |
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| author | Bulj, Aleksandar Shiraki, Shobu |
| author_facet | Bulj, Aleksandar Shiraki, Shobu |
| contents | Given a smooth curve with nonzero curvature $Σ\subset \mathbb{R}^2$, let $E_Σ$ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs $(p,q)\in [1,\infty]^2$ for which the estimates $\|E_Σf\|_{L^q(Ω)}\leq C\|f\|_{L^p(Σ)}$ and $(\mathcal{R}(|E_Σf|^{q}))^{\frac{1}{q}}\leq C\|f\|_{L^p(Σ)}$ hold, where $Ω$ is a strip in $\mathbb{R}^2$ and $\mathcal{R}$ denotes the Radon transform. This work continues the study of mass concentration of $x\mapsto E_Σf(x)$ near lines in $\mathbb{R}^2$, initiated by Bennett and Nakamura and later extended by Bennett, Nakamura, and the second author, where expressions of the form $(\mathcal{R}(|E_Σf|^{2}))^{\frac{1}{2}}$ were studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier extension estimates on a strip in $\mathbb{R}^2$ Bulj, Aleksandar Shiraki, Shobu Classical Analysis and ODEs Given a smooth curve with nonzero curvature $Σ\subset \mathbb{R}^2$, let $E_Σ$ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs $(p,q)\in [1,\infty]^2$ for which the estimates $\|E_Σf\|_{L^q(Ω)}\leq C\|f\|_{L^p(Σ)}$ and $(\mathcal{R}(|E_Σf|^{q}))^{\frac{1}{q}}\leq C\|f\|_{L^p(Σ)}$ hold, where $Ω$ is a strip in $\mathbb{R}^2$ and $\mathcal{R}$ denotes the Radon transform. This work continues the study of mass concentration of $x\mapsto E_Σf(x)$ near lines in $\mathbb{R}^2$, initiated by Bennett and Nakamura and later extended by Bennett, Nakamura, and the second author, where expressions of the form $(\mathcal{R}(|E_Σf|^{2}))^{\frac{1}{2}}$ were studied. |
| title | Fourier extension estimates on a strip in $\mathbb{R}^2$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.20463 |