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

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}, $\mathbf{\text{316}}$, 255-291 (2017). The damping estimates obtained in this paper are of independent interest.