On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces
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 fun...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/412 |
| _version_ | 1827395712922419200 |
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| author | N.А. Bokayev А.А. Khairkulova |
| author_facet | N.А. Bokayev А.А. Khairkulova |
| author_sort | N.А. Bokayev |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-03-08T18:38:44Z |
| format | Article |
| id | doaj.art-27dc3211713a413494f656839a7066b2 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:44Z |
| publishDate | 2021-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-27dc3211713a413494f656839a7066b22023-12-29T10:20:05ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-03-01101110.31489/2021m1/17-24On the boundedness of the fractional maximal operator on global Orlicz-Morrey spacesN.А. BokayevА.А. Khairkulova 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. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/412Orlicz spaceMorrey type spacethe fractional maximal functionsthe global Orlicz-Morrey spaces |
| spellingShingle | N.А. Bokayev А.А. Khairkulova On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces Қарағанды университетінің хабаршысы. Математика сериясы Orlicz space Morrey type space the fractional maximal functions the global Orlicz-Morrey spaces |
| title | On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces |
| title_full | On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces |
| title_fullStr | On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces |
| title_full_unstemmed | On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces |
| title_short | On the boundedness of the fractional maximal operator on global Orlicz-Morrey spaces |
| title_sort | on the boundedness of the fractional maximal operator on global orlicz morrey spaces |
| topic | Orlicz space Morrey type space the fractional maximal functions the global Orlicz-Morrey spaces |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/412 |
| work_keys_str_mv | AT nabokayev ontheboundednessofthefractionalmaximaloperatoronglobalorliczmorreyspaces AT aakhairkulova ontheboundednessofthefractionalmaximaloperatoronglobalorliczmorreyspaces |