In this paper we study the LP-convergence of the Riesz means S(R)(delta)(f) for the sublaplacian on the sphere S^(2n-1) in the complex n-dimensional space C^n. We show that S(R)(delta)(f) converges to f in L(p)(S(2n-1)) when delta > delta(p) := (2n - 1)| 1/2 - 1/p | and R tends to infinity. The index delta(p) coincides with the one found by Mauceri and, with different methods, by Muller in the case of sublaplacian on the Heisenberg group. It is worth noticing that the index delta(p) depends on the topological dimension of the underlying space S^(2n-1).
L^p summability of Bochner-Riesz means for the sublaplacian on complex spheres
CASARINO, VALENTINA;
2011
Abstract
In this paper we study the LP-convergence of the Riesz means S(R)(delta)(f) for the sublaplacian on the sphere S^(2n-1) in the complex n-dimensional space C^n. We show that S(R)(delta)(f) converges to f in L(p)(S(2n-1)) when delta > delta(p) := (2n - 1)| 1/2 - 1/p | and R tends to infinity. The index delta(p) coincides with the one found by Mauceri and, with different methods, by Muller in the case of sublaplacian on the Heisenberg group. It is worth noticing that the index delta(p) depends on the topological dimension of the underlying space S^(2n-1).File in questo prodotto:
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