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

Nurzhan Bokayev, А.А. Khairkulova

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021

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DOI 10.31489/2021m1/17-24

Data confidence 70 medium

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Abstract

The article deals with the global Orlia-Morrey spaces GMΦ,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 Mα from GMΦ,ϕ,θ(Rn) in GMΨ,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.