Open AccessOn the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces
Author(s) -
Nurzhan Bokayev,
А.А. Khairkulova
Publication year - 2021
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2021m1/17-24
Subject(s) - mathematics , maximal function , maximal operator , operator (biology) , norm (philosophy) , pure mathematics , function (biology) , mathematical analysis , bounded function , biochemistry , chemistry , repressor , evolutionary biology , biology , political science , transcription factor , law , gene
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.