Estimates for a certain bilinear Fourier integral operator

In this paper, we consider the boundedness from $H^{1} \times L^{\infty}$ to $L^{1}$ of bilinear Fourier integral operators with non-degenerate phase functions and amplitudes in $BS_{1,0}^{-n/2}$. Our result gives an improvement of Rodr\'iguez-L\'opez, Rule, and Staubach's result.