Multilinear Fourier Integral operators on modulation spaces

TL;DR

This paper investigates the boundedness and continuity properties of multilinear Fourier integral and pseudo-differential operators on weighted and periodic modulation spaces, utilizing Gabor frame theory.

Contribution

It introduces new boundedness results for multilinear Fourier integral operators and bilinear pseudo-differential operators on modulation spaces, including periodic and SG-class symbols.

Findings

Boundedness of multilinear Fourier integral operators on weighted modulation spaces.

Continuity of bilinear pseudo-differential operators with SG-class symbols.

Analysis of periodic multilinear Fourier integral operators.

Abstract

In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of weighted modulation spaces. Further, we investigate the periodic multilinear Fourier integral operator. Finally, we study continuity of bilinear pseudo-differential operators on modulation spaces for certain symbol classes, namely $\textbf{SG}$-class.