Weighted estimates for bilinear fractional integral operator on the Heisenberg group

Abstract

In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group ${\mathbb{H}}^n$. We completely characterize exponents $\alpha ,\beta$ and $\gamma$ such that the operator is bounded from $L^p({\mathbb{H}}^n,|x{|}^{\alpha p})\times L^q({\mathbb{H}}^n,|x{|}^{\beta q})$ to $L^r({\mathbb{H}}^n,|x{|}^{-\gamma r})$.