Department of mathematics, University of Mazandaran, babolsar, Iran.
We consider the bilinear Fourier integral operator
S(f, g)(x) =
ei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,
on modulation spaces. Our aim is to indicate this operator is well defined on
S(Rd) and shall show the relationship between the bilinear operator and BFIO on