Restriction and Kakeya maximal estimates in $\mathbb{R}^4$
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911291963080704 |
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| author | Borges, Tainara Chan, Tiklung Chen, Mingfeng Liu, Diankun Xi, Yakun Zhan, Yufei |
| author_facet | Borges, Tainara Chan, Tiklung Chen, Mingfeng Liu, Diankun Xi, Yakun Zhan, Yufei |
| contents | By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier restriction problem and the Bochner--Riesz problem, extending the range to $p > 2 + \frac{200}{251}$ in $\mathbb{R}^4$. Moreover, leveraging the two-ends Furstenberg estimate in the plane, we also obtain a Kakeya maximal estimate in $\mathbb{R}^4$ at dimension $3.054$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restriction and Kakeya maximal estimates in $\mathbb{R}^4$ Borges, Tainara Chan, Tiklung Chen, Mingfeng Liu, Diankun Xi, Yakun Zhan, Yufei Classical Analysis and ODEs By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier restriction problem and the Bochner--Riesz problem, extending the range to $p > 2 + \frac{200}{251}$ in $\mathbb{R}^4$. Moreover, leveraging the two-ends Furstenberg estimate in the plane, we also obtain a Kakeya maximal estimate in $\mathbb{R}^4$ at dimension $3.054$. |
| title | Restriction and Kakeya maximal estimates in $\mathbb{R}^4$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.22824 |