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

2008/08/02 by Karlovich, Alexei Yu.
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0808.0258

Abstract

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights φ_t,γ(τ)=|(τ-t)^γ|, where γ is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point t and γ is not real, then φ_t,γ is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko.

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