Compactness of Commutators for Riesz Potential on Local Morrey-type spaces
The paper considers Morrey-type local spaces from LM^w_pθ. The main work is the proof of the commutator compactness theorem for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. We also give new sufficient conditions for the commutator to be bounded for the...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2023-110-2/09.pdf |
| _version_ | 1797788606534778880 |
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| author | D.T. Matin T.B. Akhazhanov A. Adilkhanov |
| author_facet | D.T. Matin T.B. Akhazhanov A. Adilkhanov |
| author_sort | D.T. Matin |
| collection | DOAJ |
| description | The paper considers Morrey-type local spaces from LM^w_pθ. The main work is the proof of the commutator compactness theorem for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b, Iα] in local Morrey-type spaces LM^w_pθ, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LM^w_pθ. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b, I_α]. Similar results were obtained for global Morrey-type spaces GM^w_pθ and for generalized Morrey spaces M^w_p. |
| first_indexed | 2024-03-13T01:38:56Z |
| format | Article |
| id | doaj.art-82c17524a79741d5a39cf0fe0e6808cc |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-13T01:38:56Z |
| publishDate | 2023-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-82c17524a79741d5a39cf0fe0e6808cc2023-07-03T19:16:28ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-06-0111029310310.31489/2023M2/93-103Compactness of Commutators for Riesz Potential on Local Morrey-type spacesD.T. MatinT.B. AkhazhanovA. Adilkhanov The paper considers Morrey-type local spaces from LM^w_pθ. The main work is the proof of the commutator compactness theorem for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b, I_α] in local Morrey-type spaces from LM^w1_pθ to LM^w2_qθ. In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b, Iα] in local Morrey-type spaces LM^w_pθ, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LM^w_pθ. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b, I_α]. Similar results were obtained for global Morrey-type spaces GM^w_pθ and for generalized Morrey spaces M^w_p.https://mathematics-vestnik.ksu.kz/apart/2023-110-2/09.pdf |
| spellingShingle | D.T. Matin T.B. Akhazhanov A. Adilkhanov Compactness of Commutators for Riesz Potential on Local Morrey-type spaces Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Compactness of Commutators for Riesz Potential on Local Morrey-type spaces |
| title_full | Compactness of Commutators for Riesz Potential on Local Morrey-type spaces |
| title_fullStr | Compactness of Commutators for Riesz Potential on Local Morrey-type spaces |
| title_full_unstemmed | Compactness of Commutators for Riesz Potential on Local Morrey-type spaces |
| title_short | Compactness of Commutators for Riesz Potential on Local Morrey-type spaces |
| title_sort | compactness of commutators for riesz potential on local morrey type spaces |
| url | https://mathematics-vestnik.ksu.kz/apart/2023-110-2/09.pdf |
| work_keys_str_mv | AT dtmatin compactnessofcommutatorsforrieszpotentialonlocalmorreytypespaces AT tbakhazhanov compactnessofcommutatorsforrieszpotentialonlocalmorreytypespaces AT aadilkhanov compactnessofcommutatorsforrieszpotentialonlocalmorreytypespaces |