Damping estimates for oscillatory integral operators with real-analytic phases and its applications

TL;DR

This paper develops sharp damping estimates for one-dimensional oscillatory integral operators with real-analytic phases, providing new proofs of existing $L^p$ estimates and introducing results of independent interest.

Contribution

It introduces novel damping estimates for oscillatory integral operators with real-analytic phases and offers a new proof of known sharp $L^p$ bounds.

Findings

Established endpoint estimates for damped oscillatory operators

Provided a new proof of Xiao's sharp $L^p$ estimates

Damping estimates are of independent mathematical interest

Abstract

In this paper, we investigate sharp damping estimates for a class of one dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give a new proof of the sharp $L^p$ estimates which have been proved by Xiao in Endpoint estimates for one-dimensional oscillatory integral operators, \emph{Advances in Mathematics}, \textbf{316}, 255-291 (2017). The damping estimates obtained in this paper are of independent interest.