  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 $L^{r}(\mathbb{H}^n, |x|^{-\gamma r})$.
