An endpoint estimate for the discrete spherical maximal function

Abstract

We prove that the discrete spherical maximal function extends to a bounded operator from $L^{d/(d-2),1}(\mathbb {Z}^d)$ to $L^{d/(d-2),\infty }(\mathbb {Z}^d)$ in dimensions $d\geq 5$. This is an endpoint estimate for a recent theorem of Magyar, Stein and Wainger.

Locations

• Proceedings of the American Mathematical Society - View - PDF