Oleksiy Karlovych

Citation:

Karlovich, Alexei Yu. "Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves." Mathematische Nachrichten. 283 (2010): 85-93.

Abstract:

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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