This talk presents Theorem 4.1 in ‘On Trilinear Oscillatory Integral Inequalities and Related Topics’ by Michael Christ (arXiv:2007.12753), and compares it to previous results on similar multilinear oscillatory integral inequalities by Phong-Stein-Sturm and Gilula-Gressman-Xiao. The proof consists of various reduction steps, a microlocal decomposition (Section 7), a bifurcation in the decomposition (Section 12) and a sublevel set estimate (Section 13, also explained in an analogous setting in Section 9-11).
MSC classes: 42B20, 26D15