Riesz means and bilinear Riesz means on H-type groups

Abstract

In this paper, we investigate the Riesz means Sδ and the bilinear Riesz means Sα associated to the sublaplacian on H-type groups. We obtain the Lp-boundedness of Sδ by using the restriction theorem on H-type groups. Our result is different from that on Heisenberg groups. We prove that Sα is bounded from Lp1×Lp2 into Lp for 1≤p1,p2≤∞ and 1/p=1/p1+1/p2 when α is larger than a suitable smoothness index α(p1,p2). Because we consider H-type groups with the center dimension larger than one, it is necessary to use some different techniques from that for Heisenberg groups.