Local Smoothing Estimate For A Class Of Fourier Integral Operators Satisfying Homogeneous Carleson-Sj(?)lin Conditions

In this dissertation,we are devoted to studying the local smoothing esti-mate for a class of Fourier integral operators satisfying homogeneous Carleson-Sj(?)lin condition which contains two parts:the nondegeneracy condition and the curvature condition.By establishing certain kind of square function estimate,we improve the previous result of Mockenhaupt Seeger and Sogge[41,J.Amer.Math.Soc.6(1):65-130.1993.| on the local smoothing property of Fourier integral operators.The main ingredients of the proof are bilinear oscillatory in-tegral estimates,multilinear oscillatory integral estimate and variable coefficient Sj(?)lin inequality.