  We study the bilinear fractional integral considered by Kenig and Stein,
where linear combinations of variables with matrix coefficients are involved.
Under more general settings, we give a complete characterization of the
corresponding parameters for which the bilinear fractional integral is bounded
from $L^{p_1}(\mathbb R^{n_1}) \times L^{p_2}(\mathbb R^{n_2})$ to $L^q(\mathbb
R^m)$.
