Remark on the Boundedness of the Cauchy Singular Integral Operator on Variable Lebesgue Spaces with Radial Oscillating Weights
Classical Analysis and ODEs
2009-04-02 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0804.3880,
title = {Remark on the Boundedness of the Cauchy Singular Integral Operator on Variable Lebesgue Spaces with Radial Oscillating Weights},
author = {Alexei Yu. Karlovich},
journal= {arXiv preprint arXiv:0804.3880},
year = {2009}
}
Comments
8 pages, the case of open curves is added