Document Type : Research Paper

Authors

• M. Alimohammady
• F. Fattahi

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

Abstract

We consider the bilinear Fourier integral operator
$$S_{\sigma }(f,g)={\int }_{{\mathbb{R}}^d}{\int }_{{\mathbb{R}}^d}{e}^{i{\varphi }_1(x,\xi )}{e}^{i{\varphi }_2(x,\eta )}\sigma (x,\xi ,\eta )\hat{f}(\xi )\hat{g}(\eta )d\xi d\eta$$
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