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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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 |
| Summary: | 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. |
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| ISSN: | 0972-6802 |