Endpoint compactness of singular integrals and perturbations of the Cauchy integral

摘要

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