Almost everywhere convergence of Riesz means on noncompact symmetric spaceSL(3,H)/Sp(3)

LetG/K be the noncompact Riemannian symmetric spaceSL(3,H)/Sp(3). We shall prove in this paper that forf∈L ^p(SL(3,H)/Sp(3)), 1≤p≤2, the Riesz means of orderz off with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge tof for Rez >δ(n,p). The critical index δ(n,p) is the same as in the classical Stein's result for Euclidean space, and as in the noncompact symmetric spaces of rank one and of complex type. Partially supported by National Natural Science Foundation of China