Riesz means on locally symmetric spaces

Abstract

We prove that for a certain class of $n$ dimensional rank one locally symmetric spaces, if $f\in L^p$, $1\le p\le 2$, then the Riesz means of order $z$ of $f$ converge to $f$ almost everywhere, for $\mathrm{Re}z>(n-1)(1/p-1/2).$