BMO–VMO results for fractional integrals in variable exponent Morrey spaces. (July 2019) - Rafeiro, Humberto; Samko, Stefan
Abstract: 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 V L p ⋅, λ ⋅ Ω into VMO ( Ω ). The results seem to be new even when p and λ are constant.