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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832546231943954432 |
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| author | Alexei Yu. Karlovich |
| author_facet | Alexei Yu. Karlovich |
| author_sort | Alexei Yu. Karlovich |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e360876576b4424ea319de72574e79c1 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-e360876576b4424ea319de72574e79c12025-02-03T07:23:32ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2009/438146 |
| work_keys_str_mv | AT alexeiyukarlovich remarkontheboundednessofthecauchysingularintegraloperatoronvariablelebesguespaceswithradialoscillatingweights |