Summary
Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f ε 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.
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The first author was supported by funds of the Ministero della Pubblica Istruzione. The work was done while the second author was a member of the Mathematical Sciences Research Institute at Berkeley, with a fellowship from the Consiglio Nazionale delle Ricerehe.
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Giulini, S., Mauceri, G. Almost everywhere convergence of riesz means on certain noncompact symmetric spaces. Annali di Matematica pura ed applicata 159, 357–369 (1991). https://doi.org/10.1007/BF01766309
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DOI: https://doi.org/10.1007/BF01766309