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Karlovych, Oleksiy, and Eugene Shargorodsky. "A remark on Toeplitz and Laurent operators acting on l-p spaces with power weights." Linear Algebra and Applications (In Press).Website
Karlovich, Alexei Yu. "Remark on the boundedness of the Cauchy singular integral operator on variable Lebesgue spaces with radial oscillating weights." Journal of Function Spaces and Applications. 7 (2009): 301-311. AbstractWebsite

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.

Karlovych, Oleksiy, and Eugene Shargorodsky. "Remark on singular integral operators of convolution type on rearrangement-invariant Banach function spaces." Real Analysis Exchange. 48.1 (2023): 139-148.Website