Estimates for a certain bilinear Fourier integral operator

TL;DR

This paper establishes new boundedness results for a class of bilinear Fourier integral operators, improving previous bounds by considering specific phase functions and amplitude classes.

Contribution

It provides improved boundedness estimates for bilinear Fourier integral operators with non-degenerate phases and specific amplitude classes, advancing the theoretical understanding.

Findings

Boundedness from H^1 x L^∞ to L^1 established

Improves upon previous results by Rodrf3guez-Lf3pez, Rule, and Staubach

Results apply to operators with non-degenerate phase functions

Abstract

In this paper, we consider the boundedness from $H^{1} \times L^{\infty}$ to $L^{1}$ of bilinear Fourier integral operators with non-degenerate phase functions and amplitudes in $BS_{1,0}^{-n/2}$. Our result gives an improvement of Rodr\'iguez-L\'opez, Rule, and Staubach's result.