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 L2(R) 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.

Keywords

• Almost orthogonal theorem
• Fourier oscillatory integrals
• Norm decay rate