Boundedness of New Type Fourier Integral Operators with Product Structure

TL;DR

This paper studies a new class of Fourier integral operators with weaker symbols, proving they are bounded on classical $L^p$ spaces and from $H^1$ to $L^1$, using traditional Hardy spaces.

Contribution

It introduces a class of Fourier integral operators with multi-parameter differential inequalities and proves their boundedness in classical function spaces.

Findings

Operators are bounded on $L^p$ spaces.

Operators are bounded from $H^1$ to $L^1$.

Hardy space used is the traditional single-parameter type.

Abstract

We investigate a class of Fourier integral operators with weakened symbols, which satisfy a multi-parameter differential inequality in $\R^n$. We establish that these operators retain the classical $L^p$ boundedness and the $H^1$ to $L^1$ boundedness. Notably, the Hardy space considered here is the traditional single-parameter Hardy space rather than a product Hardy space.