Bilinear Fractional Integral Operators

Abstract: 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 $L^q(\mathbb R^m)$.