| 关于Marcinkiewicz积分高阶交换子在弱Hardy空间中的有界性 |
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| 引用本文： | 张松艳,周根娇,陶祥兴.关于Marcinkiewicz积分高阶交换子在弱Hardy空间中的有界性[J].纯粹数学与应用数学,2010,26(1):42-50,63. |
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| 作者姓名： | 张松艳 周根娇 陶祥兴 |
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| 作者单位： | 浙江科技学院经管学院,浙江,杭州,310023;宁波大学数学系,浙江,宁波,315211;赣南师范学院科技学院,江西,赣州,341000;浙江科技学院数学系,浙江,杭州,310023 |
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| 基金项目： | 国家自然科学基金(10771110,10471069);;宁波市自然科学基金(2009A610084) |
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| 摘 要： | 设μΩ带非光滑核Ω的Marcinkiewicz积分算子，m是正整数，肛μΩ,b^m是算子μΩ与BMO函数b产生的m阶交换子．利用原子分解和Littlewood—Paley技术，该文建立了高阶交换子μΩ,b^m在一类原子型弱Hardy空间WHb,m^p（0〈p≤1）中的有界性．
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| 关 键 词： | Marcinkiewicz积分 高阶交换子 原子型弱Hardy空间 |
On boundedness of the high order commutators of Marcinkiewicz integrals on weak Hardy spaces of atom type |
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| ZHANG Song-yan,ZHOU Gen-jiao,TAO Xiang-xing.On boundedness of the high order commutators of Marcinkiewicz integrals on weak Hardy spaces of atom type[J].Pure and Applied Mathematics,2010,26(1):42-50,63. |
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| Authors: | ZHANG Song-yan ZHOU Gen-jiao TAO Xiang-xing |
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| Institution: | 1;2;1.Department of Economics;Zhejiang University of Science and Technology;Hangzhou 310023;China;2.Department of Mathematics;Ningbo University;Ningbo 315211;3.School of Science and Technology;Gannan Normal University;Gannan 341000;4.Department of Mathematics;China |
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| Abstract: | Let μΩ be the Marcinkiewicz integral operator with the non-smooth kernel 12, m be any positive integer, and μΩ,b^m be the commutator of μΩ and b ∈ BMO（R^n）. The boundedness for the high order commutator μΩ,b^m on some weak Hardy space of atom type, WHb,m^p（0 〈 p 〈 1）, has been obtained by the atomic decomposition and the Littlewood-Paley＇s technique. |
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| Keywords: | Marcinkiewicz integral high order commutator weak Hardy space of atom type |
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