In this paper we study the Lp-convergence of the Riesz means SRδ(f) for the sublaplacian on the sphere S2n - 1 in the complex n-dimensional space ℂn. We show that SR δ(f) converges to f in Lp(S2n - 1) when δ > δ (p)(2n - 1)1/2 - 1/p and R→ + ∞. The index (p) coincides with the one found by Mauceri and, with different methods, by Müller in the case of sublaplacian on the Heisenberg group. It is worth noticing that the index δ(p) depends on the topological dimension of the underlying space S2n-1.
$L^p$-summability of Riesz means for the sublaplacian on complex spheres / V. Casarino, M.M. Peloso. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 83:1(2011), pp. 137-152. [10.1112/jlms/jdq067]
$L^p$-summability of Riesz means for the sublaplacian on complex spheres
M.M. Peloso
2011
Abstract
In this paper we study the Lp-convergence of the Riesz means SRδ(f) for the sublaplacian on the sphere S2n - 1 in the complex n-dimensional space ℂn. We show that SR δ(f) converges to f in Lp(S2n - 1) when δ > δ (p)(2n - 1)1/2 - 1/p and R→ + ∞. The index (p) coincides with the one found by Mauceri and, with different methods, by Müller in the case of sublaplacian on the Heisenberg group. It is worth noticing that the index δ(p) depends on the topological dimension of the underlying space S2n-1.
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