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arXiv · 2609.17466

Improved $L^p$ bounds for the helical maximal function in dimensions $n \geq 5$

Changkeun Oh·Jaehyun Woo
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Abstract

Let $n \geq 5$. We prove that the helical maximal operator is bounded on $L^p(\mathbb{R}^n)$ for some $p<2n-4$. This improves the previously known range $p>2n-4$ obtained by Gan-Maldague-Oh. As observed by Beltran-Hickman, the exponent $2n-4$ is the natural limit of the standard local smoothing method.

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Changkeun Oh, Jaehyun Woo. 2026-09-15. Improved $L^p$ bounds for the helical maximal function in dimensions $n \geq 5$. https://arxiv.org/abs/2609.17466

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