Almost everywhere convergence of riesz means on certain noncompact symmetric spaces

Abstract

Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f e Lp, 1⩽p⩽2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to falmost everywhere for Re(z)>δ(l, p). The critical index δ(l, p) is the same as in the classical result of Stein in the Euclidean case.