Bilinear Riesz means on the Heisenberg group

In this article, we investigate the bilinear Riesz means Sα associated with the sublaplacian on the Heisenberg group. We prove that the operator Sα is bounded from \({L^{{p_1}}} \times {L^{{p_2}}}\) into Lp for 1 ⩽ p1,p2 ⩽ and 1/p = 1/p1 + 1/p2 when α is larger than the suitable smoothness index α(p1, p2). There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem. We use some special techniques to obtain lower indices α(p1,p2).