Bilinear Fourier integral operator and its boundedness

Alimohammady, M.; Fattahi, F.

doi:10.22075/ijnaa.2011.109

Bilinear Fourier integral operator and its boundedness

Document Type : Research Paper

Authors

M. Alimohammady

F. Fattahi

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

10.22075/ijnaa.2011.109

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

Fourier integral operator

boundedness

modulation spaces