Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent

Abstract

We prove the boundedness of the maximal operator ℳΓ in the spaces Lp(·)(Γ, ρ) with variable exponent p(t) and power weight ρ on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Γ.