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

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

2008-08-02

arxiv.org/abs/0808.0258v1

Mathematics

Classical Analysis and ODEs

13 pages

Scientific paper

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights $\varphi_{t,\gamma}(\tau)=|(\tau-t)^\gamma|$, 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 $\varphi_{t,\gamma}$ 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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