Weighted weak type $(1,1)$ estimates for oscillatory singular integrals with Dini kernels

TL;DR

This paper establishes weighted weak type (1,1) bounds for oscillatory singular integrals with Dini-continuous kernels under A_1-weight conditions.

Contribution

It provides the first weighted weak (1,1) estimates for a class of oscillatory singular integrals with Dini kernels.

Findings

Proves weighted weak (1,1) bounds for oscillatory singular integrals.

Extends classical results to kernels with Dini continuity.

Applicable to A_1-weighted function spaces.

Abstract

We consider $A_1$-weights and prove weighted weak type $(1,1)$ estimates for oscillatory singular integrals with kernels satisfying a Dini condition.