Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces
The authors study the boundedness for a large class of sublinear operator T generated by Calderón-Zygmund operator on generalized Morrey spaces Mp,φ. As an application of this result, the boundedness of the commutator of sublinear operators Ta on generalized Morrey spaces is obtained. In the case a∈...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/356041 |
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| author | Vagif S. Guliyev Seymur S. Aliyev Turhan Karaman |
| author_facet | Vagif S. Guliyev Seymur S. Aliyev Turhan Karaman |
| author_sort | Vagif S. Guliyev |
| collection | DOAJ |
| description | The authors study the boundedness for a large class of sublinear operator T generated by Calderón-Zygmund operator on generalized Morrey spaces Mp,φ. As an application of this result, the boundedness of the commutator of sublinear operators Ta on generalized Morrey spaces is obtained. In the case a∈BMO(ℝn), 1<p<∞ and Ta is a sublinear operator, we find the sufficient conditions on the pair (φ1,φ2) which ensures the boundedness of the operator Ta from one generalized Morrey space Mp,φ1 to another Mp,φ2. In all cases, the conditions for the boundedness of Ta are given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity of φ1,φ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator. |
| format | Article |
| id | doaj-art-38e2496b2672466d912f3f3006537a92 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-38e2496b2672466d912f3f3006537a922025-02-03T07:25:53ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/356041356041Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey SpacesVagif S. Guliyev0Seymur S. Aliyev1Turhan Karaman2Department of Mathematics, Ahi Evran University, 40100 Kirsehir, TurkeyInstitute of Mathematics and Mechanics of NAS of Azerbaijan, Baku 1141, AzerbaijanDepartment of Mathematics, Ahi Evran University, 40100 Kirsehir, TurkeyThe authors study the boundedness for a large class of sublinear operator T generated by Calderón-Zygmund operator on generalized Morrey spaces Mp,φ. As an application of this result, the boundedness of the commutator of sublinear operators Ta on generalized Morrey spaces is obtained. In the case a∈BMO(ℝn), 1<p<∞ and Ta is a sublinear operator, we find the sufficient conditions on the pair (φ1,φ2) which ensures the boundedness of the operator Ta from one generalized Morrey space Mp,φ1 to another Mp,φ2. In all cases, the conditions for the boundedness of Ta are given in terms of Zygmund-type integral inequalities on (φ1,φ2), which do not assume any assumption on monotonicity of φ1,φ2 in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular pseudodifferential operators, Littlewood-Paley operator, Marcinkiewicz operator, and Bochner-Riesz operator.http://dx.doi.org/10.1155/2011/356041 |
| spellingShingle | Vagif S. Guliyev Seymur S. Aliyev Turhan Karaman Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces Abstract and Applied Analysis |
| title | Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces |
| title_full | Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces |
| title_fullStr | Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces |
| title_full_unstemmed | Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces |
| title_short | Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces |
| title_sort | boundedness of a class of sublinear operators and their commutators on generalized morrey spaces |
| url | http://dx.doi.org/10.1155/2011/356041 |
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