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 Hörmander symbol classes $S_{\rho ,\delta }^m$ for all $0\le \rho \le 1$ and $0\le \delta <1$, a notable example is the Schrödinger 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.