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

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

2008-11-19

arxiv.org/abs/0811.3087v1

Mathematics

Functional Analysis

Rapporto interno Politecnico di Torino, Novembre 2008

Scientific paper

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.

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