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

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

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

Classical Analysis and ODEs 2025-12-01 v1

Authors: Tainara Borges , Tiklung Chan , Mingfeng Chen , Diankun Liu , Yakun Xi , Yufei Zhan

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 $3.054$ .

Keywords

fourier restriction estimates bound

Cite

@article{arxiv.2511.22824,
  title  = {Restriction and Kakeya maximal estimates in $\mathbb{R}^4$},
  author = {Tainara Borges and Tiklung Chan and Mingfeng Chen and Diankun Liu and Yakun Xi and Yufei Zhan},
  journal= {arXiv preprint arXiv:2511.22824},
  year   = {2025}
}

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

Abstract

Keywords

Cite

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