Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f ∈ L^p, 1≤p≤2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to f almost everywhere for Re(z)>d(l,p). The critical index d(l,p) is the same as in the classical result of Stein in the Euclidean case.
Almost everywhere convergence of Riesz means on certain non compact symmetric spaces
GIULINI, SAVERIO;MAUCERI, GIANCARLO
1991-01-01
Abstract
Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f ∈ L^p, 1≤p≤2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to f almost everywhere for Re(z)>d(l,p). The critical index d(l,p) is the same as in the classical result of Stein in the Euclidean case.
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