A Generalization of Exponential Class and Its Applications
A function space, Lθ,∞)(Ω), 0≤θ<∞, is defined. It is proved that Lθ,∞)(Ω) is a Banach space which is a generalization of exponential class. An alternative definition of Lθ,∞)(Ω) space is given. As an application, we obtain weak monotonicity property for very weak solutions of 𝒜-harmonic equation...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/476309 |
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| author | Hongya Gao Chao Liu Hong Tian |
| author_facet | Hongya Gao Chao Liu Hong Tian |
| author_sort | Hongya Gao |
| collection | DOAJ |
| description | A function space, Lθ,∞)(Ω), 0≤θ<∞, is defined. It is proved that Lθ,∞)(Ω) is a Banach space which is a generalization of exponential class. An alternative definition of Lθ,∞)(Ω) space is given. As an application, we obtain weak monotonicity property for very weak solutions of 𝒜-harmonic equation with variable coefficients under some suitable conditions related to Lθ,∞)(Ω), which provides a generalization of a known result due to Moscariello. A weighted space Lwθ,∞)(Ω) is also defined, and the boundedness for the Hardy-Littlewood maximal operator Mw and a Calderón-Zygmund operator T with respect to Lwθ,∞)(Ω) is obtained. |
| format | Article |
| id | doaj-art-059431da088e4616b4281a91fd00a3c1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-059431da088e4616b4281a91fd00a3c12025-02-03T01:21:14ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/476309476309A Generalization of Exponential Class and Its ApplicationsHongya Gao0Chao Liu1Hong Tian2College of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaCollege of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaCollege of Mathematics and Computer Science, Hebei University, Baoding 071002, ChinaA function space, Lθ,∞)(Ω), 0≤θ<∞, is defined. It is proved that Lθ,∞)(Ω) is a Banach space which is a generalization of exponential class. An alternative definition of Lθ,∞)(Ω) space is given. As an application, we obtain weak monotonicity property for very weak solutions of 𝒜-harmonic equation with variable coefficients under some suitable conditions related to Lθ,∞)(Ω), which provides a generalization of a known result due to Moscariello. A weighted space Lwθ,∞)(Ω) is also defined, and the boundedness for the Hardy-Littlewood maximal operator Mw and a Calderón-Zygmund operator T with respect to Lwθ,∞)(Ω) is obtained.http://dx.doi.org/10.1155/2013/476309 |
| spellingShingle | Hongya Gao Chao Liu Hong Tian A Generalization of Exponential Class and Its Applications Abstract and Applied Analysis |
| title | A Generalization of Exponential Class and Its Applications |
| title_full | A Generalization of Exponential Class and Its Applications |
| title_fullStr | A Generalization of Exponential Class and Its Applications |
| title_full_unstemmed | A Generalization of Exponential Class and Its Applications |
| title_short | A Generalization of Exponential Class and Its Applications |
| title_sort | generalization of exponential class and its applications |
| url | http://dx.doi.org/10.1155/2013/476309 |
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