Riesz means on locally symmetric spaces

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

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