Functional Analysis and Applications Seminar 

26/09/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Universidade Nova de Lisboa

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

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