Weighted weak (1,1) estimates hold for oscillatory singular integrals with Dini kernels under A1 weights.
Sato,Weighted weak type(1,1)estimates for oscillatory singular integrals, Feb
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Weighted weak type $(1,1)$ estimates for oscillatory singular integrals with Dini kernels
Weighted weak (1,1) estimates hold for oscillatory singular integrals with Dini kernels under A1 weights.