Regularity of multi-parameter Fourier integral operator

TL;DR

This paper extends sharp L^p boundedness results for a family of Fourier integral operators to multi-parameter settings on product spaces, broadening understanding of their regularity properties.

Contribution

It generalizes existing results by allowing symbols to satisfy multi-parameter differential inequalities, applying to product spaces.

Findings

Extended sharp L^p bounds to multi-parameter Fourier integral operators

Established regularity results on product spaces

Generalized previous single-parameter results

Abstract

We study a family of Fourier integral operators, by allowing their symbols to satisfy a multi-parameter differential inequality. We extend the sharp L^p-result obtained by Seeger, Sogge and Stein to product spaces.