Contributions to the Fractional Hardy Integral Inequality
This article makes three contributions to the fractional Hardy integral inequality. First, we refine an existing result in the literature by improving the main constant and relaxing some assumptions on the parameters. We then propose a fractional-type Hardy integral inequality for an under-studied c...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2025-03-01
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| Series: | Universal Journal of Mathematics and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4388490 |
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| _version_ | 1850282689575256064 |
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| author | Christophe Chesneau |
| author_facet | Christophe Chesneau |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
| description | This article makes three contributions to the fractional Hardy integral inequality. First, we refine an existing result in the literature by improving the main constant and relaxing some assumptions on the parameters. We then propose a fractional-type Hardy integral inequality for an under-studied case, with a significant adaptation of the existing general proof. Finally, a version of this result is established when the integral domain is finite. The proofs are given in detail, with the exact expression of the constants involved at each step. We also mention that almost no intermediate results are used. |
| format | Article |
| id | doaj-art-541c8763f54449a28ef9be3e8efcbf00 |
| institution | OA Journals |
| issn | 2619-9653 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj-art-541c8763f54449a28ef9be3e8efcbf002025-08-20T01:47:54ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532025-03-0181212910.32323/ujma.15901541225Contributions to the Fractional Hardy Integral InequalityChristophe Chesneau0https://orcid.org/0000-0002-1522-9292Université de Caen-NormandieThis article makes three contributions to the fractional Hardy integral inequality. First, we refine an existing result in the literature by improving the main constant and relaxing some assumptions on the parameters. We then propose a fractional-type Hardy integral inequality for an under-studied case, with a significant adaptation of the existing general proof. Finally, a version of this result is established when the integral domain is finite. The proofs are given in detail, with the exact expression of the constants involved at each step. We also mention that almost no intermediate results are used.https://dergipark.org.tr/en/download/article-file/4388490fractional hardy integral inequalityfubini-tonelli integral theoremhardy integral inequalityintegral inequalities |
| spellingShingle | Christophe Chesneau Contributions to the Fractional Hardy Integral Inequality Universal Journal of Mathematics and Applications fractional hardy integral inequality fubini-tonelli integral theorem hardy integral inequality integral inequalities |
| title | Contributions to the Fractional Hardy Integral Inequality |
| title_full | Contributions to the Fractional Hardy Integral Inequality |
| title_fullStr | Contributions to the Fractional Hardy Integral Inequality |
| title_full_unstemmed | Contributions to the Fractional Hardy Integral Inequality |
| title_short | Contributions to the Fractional Hardy Integral Inequality |
| title_sort | contributions to the fractional hardy integral inequality |
| topic | fractional hardy integral inequality fubini-tonelli integral theorem hardy integral inequality integral inequalities |
| url | https://dergipark.org.tr/en/download/article-file/4388490 |
| work_keys_str_mv | AT christophechesneau contributionstothefractionalhardyintegralinequality |