| Characterization for commutators of n-dimensional fractional Hardy operators |
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| 引用本文： | Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1 ) Hong-bin WANG~3 ~1 School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China,~2 Department of Mathematics,Linyi Normal University,Linyi 276005,China,~3 Department of Mathematics,China University of Mining and Technology (Beijing),Beijing 100083,China. Characterization for commutators of n-dimensional fractional Hardy operators[J]. 中国科学A辑(英文版), 2007, 50(10): 1418-1426. DOI: 10.1007/s11425-007-0094-4 |
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| 作者姓名： | Zun-wei FU~(1 2) Zong-guang LIU~3 Shan-zhen LU~(1 ) Hong-bin WANG~3 ~1 School of Mathematical Sciences Beijing Normal University Beijing 100875 China ~2 Department of Mathematics Linyi Normal University Linyi 276005 China ~3 Department of Mathematics China University of Mining and Technology (Beijing) Beijing 100083 China |
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| 作者单位： | Zun-wei FU~(1，2) Zong-guang LIU~3 Shan-zhen LU~(1 ) Hong-bin WANG~3 ~1 School of Mathematical Sciences，Beijing Normal University，Beijing 100875，China;~2 Department of Mathematics，Linyi Normal University，Linyi 276005，China;~3 Department of Mathematics，China University of Mining and Technology (Beijing)，Beijing 100083，China |
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| 摘 要： | In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 ＜ p1 ＜∞, 0 ≤β＜ n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained.
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Characterization for commutators of n-dimensional fractional Hardy operators |
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| Zun-wei FU,Zong-guang LIU,Shan-zhen LU,Hong-bin WANG. Characterization for commutators of n-dimensional fractional Hardy operators[J]. Science in China(Mathematics), 2007, 50(10): 1418-1426. DOI: 10.1007/s11425-007-0094-4 |
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| Authors: | Zun-wei FU Zong-guang LIU Shan-zhen LU Hong-bin WANG |
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| Abstract: | In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 ＜ p1 ＜∞, 0 ≤β＜ n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained. |
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| Keywords: | n-dimensional fractional Hardy operator commutator C(M)O function homogeneous Herz space |
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