Bilinear sparse domination for oscillatory integral operators

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H & ouml;rmander symbol classes S-rho,delta(m) for all 0 <= rho <= 1 and 0 <= delta < 1, a notable example is the Schr & ouml;dinger operator. As a consequence, one obtains weak (1, 1) estimates, vector-valued estimates, and a wide range of weighted norm inequalities for these classes of operators.