Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces
Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces
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DOI：
10.1007/s00020-011-1904-1
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发表时间：
2011-09
影响因子：
0.8
通讯作者：
V. Guliyev;S. S. Aliyev-S.;T. Karaman;P. Shukurov
中科院分区：
文献类型：
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作者：
V. Guliyev;S. S. Aliyev-S.;T. Karaman;P. Shukurov
In this paper the authors study the boundedness for a large class of sublinear operatorsgenerated by Calderón–Zygmund operators (α= 0) and generated by Riesz potential operator (α> 0) on generalized Morrey spaces. As an application of the above result, the boundeness of the commutator of sublinear operatorson generalized Morrey spaces is also obtained. In the caseandTb,αis a sublinear operator, we find the sufficient conditions on the pairwhich ensures the boundedness of the operatorsfrom one generalized Morrey spaceto anotherwith 1/p− 1/q=α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on, which do not assume any assumption on monotonicity ofinr. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.
