On the boundedness of bilinear operators on products of Besov and Lebesgue spaces

We prove mapping properties of the form and , for certain related indices p1,p2,p3,q1,q2,α1,α2∈R, where T is a bilinear Hörmander–Mihlin multiplier or a molecular paraproduct. Applications to bilinear Littlewood–Paley theory are discussed.