English

Sharp $L^p$ bounds for the helical maximal function

Classical Analysis and ODEs 2025-07-29 v1

Abstract

We establish the Lp(R3)L^p(\mathbb{R}^3) boundedness of the helical maximal function for the sharp range p>3p>3. Our results improve the previous known bounds for p>4p>4. The key ingredient is a new microlocal smoothing estimate for averages along dilates of the helix, which is established via a square function analysis.

Keywords

Cite

@article{arxiv.2102.08272,
  title  = {Sharp $L^p$ bounds for the helical maximal function},
  author = {David Beltran and Shaoming Guo and Jonathan Hickman and Andreas Seeger},
  journal= {arXiv preprint arXiv:2102.08272},
  year   = {2025}
}

Comments

63 pages

R2 v1 2026-06-23T23:13:05.384Z