Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases

Abstract

This paper presents a new approach to the $L^2\left(R\right)$ norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.