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

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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.
Original languageUnknown
Pages (from-to)301-311
JournalJournal Of Function Spaces And Applications
Volume7
Issue number3
Publication statusPublished - 1 Jan 2009

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