proved in 1910 that $$\left\Vert S_{R}^z\left( f\right) -f\right\Vert _{p}\longrightarrow 0,\text{
as }R\longrightarrow \infty ,  \label{ri}$$[@ZYG], while for $n\geq 2$, C. Fefferman [@fef Theorem 1] proved in 1972 that (\[ri\]) is valid iff $p=2$.

In his seminal work [@STEIN27], E.M. Stein proved in 1958 that for all $n\geq 1$ and $f\in L^{p}\left( \left[ 0,1\right] ^{n}\right) $, $p\in \left( 1,2%
\right] $, then $$\left\Vert S_{R}^{z}\left( f\right) -f\right\Vert _{p}\longrightarrow 0,%
\text{ as }R\longrightarrow \infty ,  \label{st}$$whenever $\operatorname{Re}z$ is larger than the *critical index* $%
z_0(n,p)=\left( \frac{n-1}{2}\right) \left( \frac{2}{p}-1\right) $.

Since then, many authors have investigated the almost everywhere convergence of Riesz means. They have already been extensively studied in the case of $%
\mathbb{R}^{n}$ ([@CHRIST7; @CHRIST8; @STEIN27; @STEIN29] as well as in the book [@DAVCHANG]). In the case of elliptic differential operators on compact manifolds they are treated in ([Berard,ChristSogge,GIUTRA,HORM,SEEGER,Sogge]{}). The case of Lie groups of polynomial volume growth and of Riemannian manifolds of nonnegative curvature is studied in [@ALEXOLO; @MAR] and the case of compact semisimple Lie groups in [@CLERC2].

The rank one noncompact symmetric spaces are treated in 1991 by Giulini and Mauceri in [@GIUMA] and in 1997 the case of $SL(3,\mathbb{H})/Sp(3),$ which has rank 2, is studied in [@zhu]. Here 