Sharp local smoothing estimates for curve averages

Abstract

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^p$ boundedness of the helical maximal operator in ${\mathbb{R}}^4$, which was previously known only for ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. We also improve previously known results in higher dimensions. The main new ingredient is a novel wave envelope estimate adapted to moment curves, which is a powerful tool in the proof of the local smoothing estimate.

Section 1 has been split into Sections 1 and 2, the page layout has been adjusted, and minor typos have been corrected