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Endpoint compactness of singular integrals and perturbations of the Cauchy integral

Perfekt, Karl Mikael LU ; Pott, Sandra LU and Villarroya, Paco (2017) In Kyoto Journal of Mathematics 57(2). p.365-393
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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Kyoto Journal of Mathematics
volume
57
issue
2
pages
29 pages
publisher
Kyoto University
external identifiers
  • scopus:85019766221
  • wos:000400882600004
ISSN
2156-2261
DOI
10.1215/21562261-3821837
language
English
LU publication?
yes
id
f4f39d77-9594-4572-9b0e-9b552c15f3c1
date added to LUP
2017-06-08 13:05:18
date last changed
2024-01-28 19:48:08
@article{f4f39d77-9594-4572-9b0e-9b552c15f3c1,
  abstract     = {{<p>We prove sufficient and necessary conditions for the compactness of Calderón-Zygmund operators on the endpoint from L<sup>∞</sup> (R) into CMO(R). We use this result to prove the compactness on L<sup>p</sup> (R) with 1 &lt; p &lt; <sup>∞</sup> of a certain perturbation of the Cauchy integral on curves with normal derivatives satisfying a CMO-condition.</p>}},
  author       = {{Perfekt, Karl Mikael and Pott, Sandra and Villarroya, Paco}},
  issn         = {{2156-2261}},
  language     = {{eng}},
  month        = {{06}},
  number       = {{2}},
  pages        = {{365--393}},
  publisher    = {{Kyoto University}},
  series       = {{Kyoto Journal of Mathematics}},
  title        = {{Endpoint compactness of singular integrals and perturbations of the Cauchy integral}},
  url          = {{http://dx.doi.org/10.1215/21562261-3821837}},
  doi          = {{10.1215/21562261-3821837}},
  volume       = {{57}},
  year         = {{2017}},
}