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arXiv · 2511.22824

Restriction and Kakeya maximal estimates in $\mathbb{R}^4$

Tainara Borges·Tiklung Chan·Mingfeng Chen·Diankun Liu·Yakun Xi·Yufei Zhan
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Abstract

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 $3.054$.

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Tainara Borges, Tiklung Chan, Mingfeng Chen, Diankun Liu, Yakun Xi, Yufei Zhan. 2025-11-28. Restriction and Kakeya maximal estimates in $\mathbb{R}^4$. https://arxiv.org/abs/2511.22824

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