Spherical maximal operators on radial functions

Andreas Seeger, Stephen Wainger, James Wright

Let $A_{t}f(x)=\int f(x+ty)d\sigma (y)$ denote the spherical means in ${\mathbb{R}}^d$ ($d\sigma$ is surface measure on $S^{d-1}$, normalized to $1$). We prove sharp estimates for the maximal functio…