Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels - Hussain Al-Qassem; Leslie Cheng; Yibiao Pan (Journal of Function Spaces)
We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature.