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

Abstract

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 {L^{p}} estimates, which have been proved by Xiao in [Endpoint estimates for one-dimensional oscillatory integral operators, Adv. Math. 316 2017, 255–291]. The damping estimates obtained in this paper are of independent interest.