Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights
Recently V. Kokilashvili, N. Samko, and S. Samko have proved a sufficient condition for the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights over Carleson curves. This condition is formulated in terms of Matuszewska-Orlicz indices of we...
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Hindawi Limited
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/438146 |
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doaj-e360876576b4424ea319de72574e79c12020-11-25T01:57:11ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022009-01-017330131110.1155/2009/438146Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weightsAlexei Yu. Karlovich0Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516 Caparica, PortugalRecently V. Kokilashvili, N. Samko, and S. Samko have proved a sufficient condition for the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights over Carleson curves. This condition is formulated in terms of Matuszewska-Orlicz indices of weights. We prove a partial converse of their result.http://dx.doi.org/10.1155/2009/438146 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alexei Yu. Karlovich |
| spellingShingle |
Alexei Yu. Karlovich Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights Journal of Function Spaces and Applications |
| author_facet |
Alexei Yu. Karlovich |
| author_sort |
Alexei Yu. Karlovich |
| title |
Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights |
| title_short |
Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights |
| title_full |
Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights |
| title_fullStr |
Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights |
| title_full_unstemmed |
Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights |
| title_sort |
remark on the boundedness of the cauchy singular integral operator on variable lebesgue spaces with radial oscillating weights |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 |
| publishDate |
2009-01-01 |
| description |
Recently V. Kokilashvili, N. Samko, and S. Samko have proved a
sufficient condition for the boundedness of the Cauchy singular integral operator
on variable Lebesgue spaces with radial oscillating weights over Carleson curves.
This condition is formulated in terms of Matuszewska-Orlicz indices of weights.
We prove a partial converse of their result. |
| url |
http://dx.doi.org/10.1155/2009/438146 |
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AT alexeiyukarlovich remarkontheboundednessofthecauchysingularintegraloperatoronvariablelebesguespaceswithradialoscillatingweights |
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