2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166318We 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.13 pagesClassical Analysis and ODEsFunctional Analysis42B20text