On local and global regularity of Fourier integral operators

TL;DR

This paper reviews the local and global regularity properties of Fourier integral operators with real and complex phases across various function spaces, including local L^p, global L^2, and Colombeau's spaces.

Contribution

It provides a comprehensive review of the regularity properties of Fourier integral operators in different functional settings, highlighting recent advances.

Findings

Detailed analysis of local L^p regularity

Global L^2 regularity results

Regularity in Colombeau's spaces

Abstract

The aim of this paper is to give a review of local and global properties of Fourier integral operators with real and complex phases, in local $L^p$, global $L^2$, and in Colombeau's spaces.