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.

30pages,1figure