L^p-summability of Riesz means for the sublaplacian on complex spheres

Abstract

In this paper we study the L^p-convergence of the Riesz means for the sublaplacian on the sphere S^{2n-1} in the complex n-dimensional space C^n. We show that the Riesz means of order delta of a function f converge to f in L^p(S^{2n-1}) when delta>delta(p):=(2n-1)|1\2-1\p|. The index delta(p) improves the one found by Alexopoulos and Lohoue', $2n|1\2-1\p|$, and it coincides with the one found by Mauceri and, with different methods, by Mueller in the case of sublaplacian on the Heisenberg group.

Rapporto interno Politecnico di Torino, Novembre 2008

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