Regularity of Fourier integrals on product spaces

TL;DR

This paper investigates Fourier integral operators with multi-parameter symbols, establishing their boundedness from Hardy spaces to L^1 and deriving sharp L^p regularity results, advancing understanding of Fourier analysis on product spaces.

Contribution

It introduces a class of Fourier integral operators with multi-parameter symbol inequalities and proves their boundedness and regularity properties, extending previous results.

Findings

Operators of order -(N-1)/2 are bounded from H^1 to L^1.

Established sharp L^p-regularity results for these operators.

Extended Fourier analysis techniques to multi-parameter settings.

Abstract

We study a family of Fourier integral operators by allowing their symbols to satisfy a multi-parameter differential inequality on R^N. We show that these operators of order -(N-1)/2 are bounded from classical, atom decomposable H^1-Hardy space to L^1(R^N). Consequently, we obtain a sharp L^p-regularity result due to Seeger, Sogge and Stein.