Bilinear sparse domination for oscillatory integral operators

Abstract

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 $$S^m_{\rho ,\delta }$$ S ρ , δ m for all $$0\le \rho \le 1$$ 0 ≤ ρ ≤ 1 and $$0\le \delta < 1$$ 0 ≤ δ < 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.