A Seeger–Sogge–Stein theorem for bilinear Fourier integral operators

Abstract

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in S1,0m(n,2) and non-degenerate phase functions, from Lp×Lq→Lr under the assumptions that m⩽−(n−1)(|1p−12|+|1q−12|) and 1p+1q=1r. This is a bilinear version of the classical theorem of Seeger–Sogge–Stein concerning the Lp boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of quasi-Banach target spaces.