Bilinear Fourier integral operator and its boundedness

Authors

Department of mathematics, University of Mazandaran, babolsar, Iran.

Abstract

We consider the bilinear Fourier integral operator
$$S_\sigma(f,g)=\int_{\mathbb{R}^d}\int_{\mathbb{R}^d}e^{i\phi_1(x,\xi)}e^{i\phi_2(x,\eta)}\sigma(x,\xi,\eta)\hat{f}(\xi)\hat{g}(\eta)d\xi d\eta$$
on modulation spaces. Our aim is to indicate this operator is well defined on $S(\mathbb{R}^d)$ and shall show the relationship between the bilinear operator and BFIO on modulation spaces.

Keywords