PreprintCC0arXiv
Sharp helical maximal estimates in all dimensions
Abstract
We establish sharp Lp maximal estimates for averages over smooth nondegenerate curves in ℝn for p>n. More precisely, we show that for any nondegenerate curve γ in ℝn and the associated maximal operator M f(x):=supt>0 |∫−11f(x−tγ(s))χ(s) ds|, the estimate | Mf|Lp(ℝn)≲γ,p,n |f|Lp(ℝn) holds for all p>n. A new ingredient is a weighted Kakeya-type estimate.
Related
- Improved Lp bounds for the helical maximal function in dimensions n ≥ 5
- Sharp weighted estimates for the multilinear maximal operator
- Sharp Lp estimates for the strong spherical maximal operator
- Sharp power-weight estimates for the fractional spherical maximal operator
- Sharp lower bounds for the periodic maximal Schrödinger operator in higher dimensions
BibTeX
@misc{gan2026sharp,
title = {{Sharp helical maximal estimates in all dimensions}},
author = {Shengwen Gan and Changkeun Oh and Jaehoon Shin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37250},
eprint = {2610.37250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37250},
note = {CC0},
}
RIS
TY - UNPB
TI - Sharp helical maximal estimates in all dimensions
AU - Shengwen Gan
AU - Changkeun Oh
AU - Jaehoon Shin
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37250
UR - https://arxiv.org/abs/2610.37250
AB - We establish sharp L^p maximal estimates for averages over smooth nondegenerate curves in ℝ^n for p>n. More precisely, we show that for any nondegenerate curve γ in ℝ^n and the associated maximal operator M f(x):=sup_t>0 |∫_−1^1f(x−tγ(s))χ(s) ds|, the estimate | Mf|_L^p(ℝ^n)≲_γ,p,n |f|_L^p(ℝ^n) holds for all p>n. A new ingredient is a weighted Kakeya-type estimate.
ER -