Weighted Hardy and Potential Operators in Morrey Spaces
We study the weighted p→q-boundedness of Hardy-type operators in Morrey spaces ℒp,λ(ℝn) (or ℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted p→q-boundedness of the Riesz potential operator. The conditions on weigh...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/678171 |
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| _version_ | 1832555348805812224 |
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| author | Natasha Samko |
| author_facet | Natasha Samko |
| author_sort | Natasha Samko |
| collection | DOAJ |
| description | We study the weighted p→q-boundedness of Hardy-type operators
in Morrey spaces ℒp,λ(ℝn) (or ℒp,λ(ℝ+1) in the one-dimensional case) for
a class of almost monotonic weights. The obtained results are applied to
a similar weighted p→q-boundedness of the Riesz potential operator.
The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case
of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights. |
| format | Article |
| id | doaj-art-984410fc69434d39a66ba0d156757742 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-984410fc69434d39a66ba0d1567577422025-02-03T05:48:29ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/678171678171Weighted Hardy and Potential Operators in Morrey SpacesNatasha Samko0Department of Mathematics, Research Center CEAF, Instituto Superior Técnico, 1049-003 Lisbon, PortugalWe study the weighted p→q-boundedness of Hardy-type operators in Morrey spaces ℒp,λ(ℝn) (or ℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weighted p→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.http://dx.doi.org/10.1155/2012/678171 |
| spellingShingle | Natasha Samko Weighted Hardy and Potential Operators in Morrey Spaces Journal of Function Spaces and Applications |
| title | Weighted Hardy and Potential Operators in Morrey Spaces |
| title_full | Weighted Hardy and Potential Operators in Morrey Spaces |
| title_fullStr | Weighted Hardy and Potential Operators in Morrey Spaces |
| title_full_unstemmed | Weighted Hardy and Potential Operators in Morrey Spaces |
| title_short | Weighted Hardy and Potential Operators in Morrey Spaces |
| title_sort | weighted hardy and potential operators in morrey spaces |
| url | http://dx.doi.org/10.1155/2012/678171 |
| work_keys_str_mv | AT natashasamko weightedhardyandpotentialoperatorsinmorreyspaces |