Bilinear Riesz means on the Heisenberg group

الأصل · EN

In this article, we investigate the bilinear Riesz means Sα associated to the sublaplacian on the Heisenberg group. We prove that the operator Sα is bounded from Lᵖ₁× Lᵖ₂ into Lᵖ for 1≤ p₁, p₂≤ ∞ and 1/p=1/p₁+1/p₂ when α is large than a 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 make use of some special techniques to obtain a lower index α(p₁,p₂).