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

TL;DR

This paper establishes improved conditions for the L^p-convergence of Riesz means of the sublaplacian on complex spheres, extending and refining previous results by other researchers.

Contribution

It provides a sharper threshold for delta ensuring convergence, matching known results in related settings using new methods.

Findings

Riesz means of order delta converge in L^p when delta > (2n-1)|1/2 - 1/p|

The threshold delta(p) improves previous bounds by Alexopoulos and Lohoue

The results align with known thresholds on the Heisenberg group

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.