Sharp L^p decay estimates for degenerate and singular oscillatory integral operators: Homogeneous polynomial phases

2021/09/29 by Xu, Shaozhen
#42B20 #47G10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.14191

Abstract

In this paper, we consider the degenerate and singular oscillatory integral operator with a singular kernel which is not a Calderón-Zygmund kernel and satisfies suitable size and derivative conditions related to a real parameter μ. For any given homogeneous polynomial phases, except monomial phases, of degreee n, we give the range of p for which the sharp decay rate -(1-μ)/(n) on L² spaces can be preserved on L^p spaces.

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