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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1494295223

Digital Object Identifier
doi:10.1215/21562261-3821837

Mathematical Reviews number (MathSciNet)
MR3648054

Zentralblatt MATH identifier
06736606

Subjects
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]

Keywords
Calderón–Zygmund operator singular integral compact operator Cauchy integral

Citation

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. https://projecteuclid.org/euclid.kjm/1494295223


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