A Remark on Weighted $(L^p ,L^r )$-Boundedness for Rough Multilinear Oscillatory Singular Integrals

Abstract

This paper studies the weighted $(L^p ,L^r)$-boundedness for a class of multilinear oscillatory singular operators with real-valued polynomial phases and rough homogeneous kernels belonging to $L{\rm log}^+L(S^{ n−1}),$ and establishes two criteria on the corresponding weighted bounds for such operators.