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Article · BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS · March 30, 2021
On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces
Nurzhan Bokayev, А.А. Khairkulova
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.
Advanced Harmonic Analysis ResearchMathematical Analysis and Transform MethodsApproximation Theory and Sequence Spacesfractional maximal operatorboundednessnecessary and sufficient conditions
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