Helical maximal function and weighted estimates

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