Riesz means and bilinear Riesz means on M\'{e}tivier groups

Abstract

In this paper, we investigate the $L^{p}$-boundedness of the Riesz means and the $L^{p_{1}}\times L^{p_{2}}\rightarrow L^{p}$ boundedness of the bilinear Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of Heisenberg groups and general H-type groups. Because general M\'{e}tivier groups only satisfy the non-degeneracy condition and have high-dimensional centre, we have to use different methods and techniques from those on Heisenberg groups and H-type groups.