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

摘要

We prove the uniform L_1 → L~(1,∞) and H_E~1→ L~1 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 H?lder condition.This H?lder condition appreciably weakens the C1 condition imposed in existing literature.