We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in $S^m_{ 1,0} (n,2)$ and non-degenerate phase functions, from $L^p \times L^q \to L^r$ under the assumptions that $m\leq -(n-1)(|\frac{ 1}{ p}-\frac{ 1}{ 2}|+|\frac{ 1}{ q}-\frac{ 1}{ 2}|)$ and $\frac{ 1}{ p}+\frac{ 1}{ q}=\frac{ 1}{ r}$. This is a bilinear version of the classical theorem of Seeger-Sogge-Stein concerning the $L^p$ boundedness of linear Fourier integral operators. Moreover, our result goes beyond the aforementioned theorem in that it also includes the case of non-Banach target spaces.
Categories: math.AP