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

Abstract

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

63 pages

Cited by in corpus (2)

• Sharp Sobolev regularity of restricted X-ray transforms
• Sharp smoothing properties of averages over curves