Helical maximal function and weighted estimates

Abstract

In this article, we characterize the range of $\hat{I}\pm$ for which the helical maximal function is bounded from $L^p(|x{|}^{\hat{I}}\pm )$ to itself for $3<p<\infty$. Our result is optimal for $4\le p<\infty ,$ except possibly at end-points.

Preliminary version. 22pp