Bilinear Fourier integral operator and its boundedness

Abstract

We consider the bilinear Fourier integral operator<br />S (f, g)(x) =<br />Z<br />Rd<br />Z<br />Rd<br />ei 1(x, )ei 2(x, ) (x, , ) ˆ f( )ˆg( )d d ,<br />on modulation spaces. Our aim is to indicate this operator is well defined on<br />S(Rd) and shall show the relationship between the bilinear operator and BFIO on<br />modulation spaces.