Abstract
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.
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Partially supported by National Natural Science Foundation of China
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Fuliu, Z. Almost everywhere convergence of Riesz means on noncompact symmetric spaceSL(3,H)/Sp(3). Acta Mathematica Sinica 13, 545–552 (1997). https://doi.org/10.1007/BF02559948
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DOI: https://doi.org/10.1007/BF02559948