Nuclearity for Fourier integral operators in $L^p$-spaces

TL;DR

This paper investigates the precise conditions under which Fourier integral operators are nuclear on $L^p$-spaces for $1<p extless{}2$, extending the understanding of nuclearity criteria across the full range of $p$ values.

Contribution

It provides sharp sufficient conditions for nuclearity of Fourier integral operators on $L^p$-spaces, expanding previous results to all $1<p< ext{infinity}$.

Findings

Established sharp nuclearity conditions for $1<p extless{}2$

Extended nuclearity criteria to all $1<p< ext{infinity}$

Compared new conditions with existing results in Cardona [2]

Abstract

In this note we study sharp sufficient conditions for the nuclearity of Fourier integral operators on $L^p$-spaces, $1< p\leq 2$. Our conditions and those presented in Cardona [2] provide a systematic investigation on the subject for all $1<p<\infty.$