Endpoint Estimates for Oscillatory Singular Integrals with H�lder Class Kernels

Abstract

We prove the uniform L1?L1,? and HE 1?L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calder�n-Zygmund kernel K(x,y) satisfying a H�lder condition. This H�lder condition appreciably weakens the C1 condition imposed in existing literature. - 2019 Hussain Al-Qassem et al.