Riesz potential and its commutators in generalized weighted Morrey spaces defined on Carleson curves

Abstract

In this paper we take up a characterization of weighted inequalities for Riesz potential and its commutators in generalized weighted Morrey spaces Mp,ϕ Mp,ϕ1 ω (Γ) defined on Carleson curves Γ with the class of weights Fp,q. We prove the boundedness of Riesz potential Iα Γ and its commutator |b,Iα Γ | from the spaces ω1 (Γ) to the spaces Mp,ϕ2 ω2 (Γ), where 0 < α < 1, 1 < p < 1 α functions, (ω1,ω2) ∈ Fp,q(Γ) and b ∈ BMO(Γ).