PreprintCC0arXiv
Improved Lp bounds for the helical maximal function in dimensions n ≥ 5
Abstract
Let n ≥ 5. We prove that the helical maximal operator is bounded on Lp(ℝn) 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.
Related
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BibTeX
@misc{oh2026improved,
title = {{Improved $L^p$ bounds for the helical maximal function in dimensions $n \geq 5$}},
author = {Changkeun Oh and Jaehyun Woo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17466},
eprint = {2609.17466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17466},
note = {CC0},
}
RIS
TY - UNPB
TI - Improved L^p bounds for the helical maximal function in dimensions n ≥ 5
AU - Changkeun Oh
AU - Jaehyun Woo
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17466
UR - https://arxiv.org/abs/2609.17466
AB - Let n ≥ 5. We prove that the helical maximal operator is bounded on L^p(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.
ER -