A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/780132 |
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| _version_ | 1849306994056364032 |
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| author | Zun Wei Fu Shan Zhen Lu Wen Yuan |
| author_facet | Zun Wei Fu Shan Zhen Lu Wen Yuan |
| author_sort | Zun Wei Fu |
| collection | DOAJ |
| description | We introduce certain type of weighted variant of Riemann-Liouville
fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions
so that commutators of weighted Hardy operators (with symbols in λ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates
of some inequalities due to Weyl and Cesàro. |
| format | Article |
| id | doaj-art-24ed2eecf0834ba593114d4febd5a9c9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-24ed2eecf0834ba593114d4febd5a9c92025-08-20T03:54:53ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/780132780132A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝnZun Wei Fu0Shan Zhen Lu1Wen Yuan2Department of Mathematics, Linyi University, Shandong, Linyi 276005, ChinaSchool of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaSchool of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaWe introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in λ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.http://dx.doi.org/10.1155/2012/780132 |
| spellingShingle | Zun Wei Fu Shan Zhen Lu Wen Yuan A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn Abstract and Applied Analysis |
| title | A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn |
| title_full | A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn |
| title_fullStr | A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn |
| title_full_unstemmed | A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn |
| title_short | A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn |
| title_sort | weighted variant of riemann liouville fractional integrals on rn |
| url | http://dx.doi.org/10.1155/2012/780132 |
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