Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) a...
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| Format: | Article |
| Language: | English |
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Sciendo
2013-06-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2013-0026 |
| _version_ | 1811272432193896448 |
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| author | Dzhabrailov Malik S. Khaligova Sevinc Z. |
| author_facet | Dzhabrailov Malik S. Khaligova Sevinc Z. |
| author_sort | Dzhabrailov Malik S. |
| collection | DOAJ |
| description | We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/|σ| ≤ 1/p-1/q≤α ((1-b) |σ|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn). |
| first_indexed | 2024-04-12T22:40:10Z |
| format | Article |
| id | doaj.art-1e8668ef5d0842cdb9c0a6c8fd6cb843 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:40:10Z |
| publishDate | 2013-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-1e8668ef5d0842cdb9c0a6c8fd6cb8432022-12-22T03:13:46ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352013-06-0121211113010.2478/auom-2013-0026Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spacesDzhabrailov Malik S.0Khaligova Sevinc Z.1Department of Mathematics Azerbaijan State Pedagogical University, Baku, AzerbaijanDepartment of Mathematics Azerbaijan State Pedagogical University, Baku, AzerbaijanWe prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/|σ| ≤ 1/p-1/q≤α ((1-b) |σ|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).https://doi.org/10.2478/auom-2013-0026anisotropic riesz potentialanisotropic fractional maximal functionanisotropic modified morrey spaceanisotropic bmo space |
| spellingShingle | Dzhabrailov Malik S. Khaligova Sevinc Z. Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space |
| title | Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces |
| title_full | Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces |
| title_fullStr | Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces |
| title_full_unstemmed | Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces |
| title_short | Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces |
| title_sort | necessary and sufficient conditions for the boundedness of the anisotropic riesz potential in anisotropic modified morrey spaces |
| topic | anisotropic riesz potential anisotropic fractional maximal function anisotropic modified morrey space anisotropic bmo space |
| url | https://doi.org/10.2478/auom-2013-0026 |
| work_keys_str_mv | AT dzhabrailovmaliks necessaryandsufficientconditionsfortheboundednessoftheanisotropicrieszpotentialinanisotropicmodifiedmorreyspaces AT khaligovasevincz necessaryandsufficientconditionsfortheboundednessoftheanisotropicrieszpotentialinanisotropicmodifiedmorreyspaces |