Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

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Abstract

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights phi(t,gamma)(tau) = |(tau - t)gamma|, where gamma is a complex number, over arbitrary Carleson Curves. If the curve has different spirality indices at the point t and gamma is not real, then phi(t,gamma) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Original languageUnknown
Pages (from-to)85-93
JournalMathematische Nachrichten
Volume283
Issue number1
DOIs
Publication statusPublished - 1 Jan 2010

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