A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space
The variable exponent Hardy inequality xβ(x)-1∫0xf(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l), f≥0 is proved assuming that the exponents p:(0,l)→(1,∞), β:(0,l)→ℝ not rapidly oscilate near origin and 1/p′(0)-β>0. The main result is a necessary and sufficient condition on p, β generalizing known results on...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/342910 |
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| author | Farman Mamedov Yusuf Zeren |
| author_facet | Farman Mamedov Yusuf Zeren |
| author_sort | Farman Mamedov |
| collection | DOAJ |
| description | The variable exponent Hardy inequality xβ(x)-1∫0xf(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l), f≥0 is proved assuming that the exponents p:(0,l)→(1,∞), β:(0,l)→ℝ not rapidly oscilate near origin and 1/p′(0)-β>0. The main result is a necessary and sufficient condition on p, β generalizing known results on this inequality. |
| format | Article |
| id | doaj-art-6b5cc6b5ee2c4399be19de095de5656e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6b5cc6b5ee2c4399be19de095de5656e2025-08-20T03:34:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/342910342910A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue SpaceFarman Mamedov0Yusuf Zeren1Mathematics and Mechanics Institute of NAS and OGRDI of SOCAR Company, 9 B. Vahabzade, 1141 Baku, AzerbaijanDepartment of Mathematics, Yildiz Technical University, Esenler, Istanbul, 34220 Davutpasha, TurkeyThe variable exponent Hardy inequality xβ(x)-1∫0xf(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l), f≥0 is proved assuming that the exponents p:(0,l)→(1,∞), β:(0,l)→ℝ not rapidly oscilate near origin and 1/p′(0)-β>0. The main result is a necessary and sufficient condition on p, β generalizing known results on this inequality.http://dx.doi.org/10.1155/2014/342910 |
| spellingShingle | Farman Mamedov Yusuf Zeren A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space Abstract and Applied Analysis |
| title | A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space |
| title_full | A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space |
| title_fullStr | A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space |
| title_full_unstemmed | A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space |
| title_short | A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space |
| title_sort | necessary and sufficient condition for hardy s operator in the variable lebesgue space |
| url | http://dx.doi.org/10.1155/2014/342910 |
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