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arXiv · 1707.03288

Endpoint compactness of singular integrals and perturbations of the Cauchy Integral

Karl-Mikael Perfekt·Sandra Pott·Paco Villarroya
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Abstract

We prove sufficient and necessary conditions for compactness of Calder\'on-Zygmund operators on the endpoint from $L^{\infty }(\mathbb R)$ into ${\rm CMO}(\mathbb R)$. We use this result to prove compactness on $L^{p}(\mathbb R)$ with $1<p<\infty $ of certain perturbations of the Cauchy integral on curves with normal derivatives satisfying a ${\rm CMO}$-condition.

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Karl-Mikael Perfekt, Sandra Pott, Paco Villarroya. 2017-07-10. Endpoint compactness of singular integrals and perturbations of the Cauchy Integral. https://doi.org/10.1215/21562261-3821837

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