Global boundedness of multilinear Fourier integral operators

TL;DR

This paper investigates the conditions under which multilinear Fourier integral operators are globally bounded on various $L^p$ spaces, extending understanding of their behavior with both smooth and rough amplitudes.

Contribution

It establishes new global boundedness results for multilinear Fourier integral operators with rough amplitudes, using iterative and decomposition techniques.

Findings

Proves global boundedness for rough linear Fourier integral operators.

Extends boundedness results to multilinear operators with rough amplitudes.

Uses decomposition and iteration methods for proofs.

Abstract

We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by proving suitable global boundedness of rough linear Fourier integral operators with amplitudes that behave as $L^{p}$ functions in the spatial variables. The bilinear and multilinear boundedness estimates are proven by using either an iteration procedure or decomposition of the amplitudes, and thereafter applying our global results for linear Fourier integral operators with rough amplitudes.