Uniform estimates for oscillatory integral operators

AbstractIn this paper we prove the uniform Lp boundedness of oscillatory singular integral operators with smooth phase functions which satisfy a certain finite-type condition. These phase functions include the class of real-analytic functions. The uniform boundedness does not hold if the finite-type condition is removed. We also obtained estimates for related operators, including an optimal L2 estimate for operators (with singular kernels) whose phase functions have non-singular Hessians