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arXiv · 0808.0258

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

Alexei Yu. Karlovich
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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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Alexei Yu. Karlovich. 2008-08-02. Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves. https://arxiv.org/abs/0808.0258

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