We consider the bilinear Fourier integral operator Sσ(f, g)(x) = Z Rd Z Rd e iφ1(x,ξ) e iφ2(x,η)σ(x, ξ, η) ˆf(ξ)ˆg(η)dξ dη, on modulation spaces. Our aim is to indicate this operator is well defined on S(R d ) and shall show the relationship between the bilinear operator and BFIO on modulation spaces.
