Bilinear Bochner-Riesz Means on Métivier groups

Abstract

In this paper, we study the $L^{p_1}(G)\times L^{p_2}(G)$ to $L^p(G)$ boundedness of the bilinear Bochner-Riesz means associated with the sub-Laplacian on Métivier group $G$ under the Hölder's relation $1/p=1/p_1+1/p_2$, $1\le p_1,p_2\le \infty$. Our objective is to obtain boundedness results, analogous to the Euclidean setting, where the Euclidean dimension in the smoothness threshold is possibly replaced by the topological dimension of the underlying Métivier group $G$.

37 pages, 2 figures