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 weights. We prove a partial converse of their result. 
Alexei Yu. Karlovich