BMO–VMO results for fractional integrals in variable exponent Morrey spaces

We prove the boundedness of the fractional integration operator of variable order α(x) in the limiting Sobolev case α(x)p(x)=n−λ(x) from variable exponent Morrey spaces L ^p⋅,λ⋅ Ω into BMO (Ω), where Ω is a bounded open set. In the case α(x)≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces VL ^p⋅,λ⋅ Ω into VMO (Ω). The results seem to be new even when p and λ are constant.