On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces

Abstract

The article deals with the global Orlia-Morrey spaces GM_Φ,ϕ,θ(Rⁿ). We find sufficient conditions on pairs of functions (ϕ, η) and (Φ, Ψ), which ensure the boundedness of the fractional maximal operator M_α from GM_Φ,ϕ,θ(Rⁿ) in GM_Ψ,η,θ(Rⁿ). It is proved that under some additional conditions on the function ϕ, the conditions obtained are also necessary. In the proof, the boundedness condition is essentially used, the maximal Hardy-Littlewood functions and the estimate of the norm of the characteristic function in global Orlicz-Morrey spaces are used.