Helical maximal function and weighted estimates

TL;DR

This paper characterizes the range of weights for which the helical maximal function is bounded on weighted L^p spaces, providing optimal results for a broad range of p.

Contribution

It offers a precise characterization of the weighted boundedness of the helical maximal function, extending understanding in harmonic analysis.

Findings

Boundedness characterized for certain alpha ranges

Optimal results established for p in [4, ∞)

Results are nearly optimal at end-points

Abstract

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