Remark on the Boundedness of the Cauchy Singular Integral Operator on Variable Lebesgue Spaces with Radial Oscillating Weights

Details Remark on the Boundedness of the Cauchy Singular Integral Operator on Variable Lebesgue Spaces with Radial Oscillating Weights Remark on the Boundedness of the Cauchy Singular Integral Operator on Variable Lebesgue Spaces with Radial Oscillating Weights

2008-04-24

arxiv.org/abs/0804.3880v2

Mathematics

Classical Analysis and ODEs

8 pages, the case of open curves is added

Scientific paper

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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