Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 438146 | https://doi.org/10.1155/2009/438146

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, vol. 7, Article ID 438146, 11 pages, 2009. https://doi.org/10.1155/2009/438146

Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights

Academic Editor: Lech Maligranda
Received01 Apr 2008

Abstract

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.

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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