Endpoint compactness of singular integrals and perturbations of the Cauchy integral

Karl Mikael Perfekt; Sandra Pott; Paco Villarroya

doi:10.1215/21562261-3821837

Endpoint compactness of singular integrals and perturbations of the Cauchy integral

Karl Mikael Perfekt, Sandra Pott, Paco Villarroya

Mathematics (Faculty of Sciences)

Research output: Contribution to journal › Article › peer-review

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 L^p (R) with 1 < p < ^∞ of a certain perturbation of the Cauchy integral on curves with normal derivatives satisfying a CMO-condition.

Original language	English
Pages (from-to)	365-393
Number of pages	29
Journal	Kyoto Journal of Mathematics
Volume	57
Issue number	2
DOIs	https://doi.org/10.1215/21562261-3821837
Publication status	Published - 2017 Jun 1

Subject classification (UKÄ)

Mathematical Analysis

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10.1215/21562261-3821837

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title = "Endpoint compactness of singular integrals and perturbations of the Cauchy integral",

abstract = "We prove sufficient and necessary conditions for the compactness of Calder{\'o}n-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.",

author = "Perfekt, {Karl Mikael} and Sandra Pott and Paco Villarroya",

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AU - Perfekt, Karl Mikael

AU - Pott, Sandra

AU - Villarroya, Paco

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

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U2 - 10.1215/21562261-3821837

DO - 10.1215/21562261-3821837

M3 - Article

AN - SCOPUS:85019766221

SN - 2156-2261

VL - 57

SP - 365

EP - 393

JO - Kyoto Journal of Mathematics

JF - Kyoto Journal of Mathematics

IS - 2

ER -

Endpoint compactness of singular integrals and perturbations of the Cauchy integral

Abstract

Subject classification (UKÄ)

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