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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |