Estimates for a certain bilinear Fourier integral operator

In this paper, we consider the boundedness from $H^1\times L^{\mathrm{\infty }}$ to $L^1$ of bilinear Fourier integral operators with non-degenerate phase functions and amplitudes in $B{S}_{1,0}^{-n\mathrm{/}2}$. Our result gives an improvement of Rodríguez-López, Rule, and Staubach’s result.