PreprintCC BY 4.0arXiv
Refinements on the Restriction and Kakeya problems range in ℝ4
Abstract
We obtain improved Fourier restriction and Kakeya maximal estimates in ℝ4. More precisely, by proving the two-ends incidence estimates TE(269/89,179/89,493/534) and TE(3.06…,3.06…,0.94…), we extend the restriction range to p>2+ 356/447 and the Kakeya maximal estimate up to dimension $3.06056$. The implications to the known lower-bounds for the Hausdorff dimension of Kakeya sets in ℝ4 and the Bochner--Riesz conjecture are also studied.
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BibTeX
@misc{moreira2026refinements,
title = {{Refinements on the Restriction and Kakeya problems range in $\mathbbR^4$}},
author = {Tiago Moreira},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06181},
eprint = {2610.06181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06181},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Refinements on the Restriction and Kakeya problems range in ℝ^4
AU - Tiago Moreira
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.06181
UR - https://arxiv.org/abs/2610.06181
AB - We obtain improved Fourier restriction and Kakeya maximal estimates in ℝ^4. More precisely, by proving the two-ends incidence estimates TE(269/89,179/89,493/534) and TE(3.06…,3.06…,0.94…), we extend the restriction range to p>2+ 356/447 and the Kakeya maximal estimate up to dimension $3.06056$. The implications to the known lower-bounds for the Hausdorff dimension of Kakeya sets in ℝ^4 and the Bochner--Riesz conjecture are also studied.
ER -