A type of oscillatory integral operator and its applications

Abstract

In this paper, we consider $L^p$- estimate for a class of oscillatory integral operators satisfying the Carleson-Sjölin conditions with further convex and straight assumptions. As applications, the multiplier problem related to a general class of hypersurfaces with nonvanishing Gaussian curvature, local smoothing estimates for the fractional Schrödinger equation and the sharp resolvent estimates outside of the uniform boundedness range are discussed.

arXiv comment30pages,1figure