Kyoto Journal of Mathematics

Endpoint compactness of singular integrals and perturbations of the Cauchy integral

Karl-Mikael Perfekt, Sandra Pott, and Paco Villarroya

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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.

Article information

Kyoto J. Math., Volume 57, Number 2 (2017), 365-393.

Received: 2 April 2015
Revised: 27 February 2016
Accepted: 15 March 2016
First available in Project Euclid: 9 May 2017

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Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 42C40: Wavelets and other special systems
Secondary: 47G10: Integral operators [See also 45P05]

Calderón–Zygmund operator singular integral compact operator Cauchy integral


Perfekt, Karl-Mikael; Pott, Sandra; Villarroya, Paco. Endpoint compactness of singular integrals and perturbations of the Cauchy integral. Kyoto J. Math. 57 (2017), no. 2, 365--393. doi:10.1215/21562261-3821837.

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