Endpoint compactness of singular integrals and perturbations of the Cauchy integral
We prove sufficient and necessary conditions for the compactness of Calderón-Zygmund operators on the endpoint from L∞ (R) into CMO(R). We use this result to prove the compactness on Lp (R) with 1 < p < ∞ of a certain perturbation of the Cauchy integral on curves with normal derivatives satisfying a CMO-condition.
