Characterization for commutators of n -dimensional fractional Hardy operators |
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Authors: | Zun-wei Fu Zong-guang Liu Shan-zhen Lu Hong-bin Wang |
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Affiliation: | (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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Abstract: | In this paper, it was proved that the commutator generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L p1 (ℝ n ) to L p2 (ℝ n ) if and only if b is a CṀO(ℝ n ) function, where 1/p 1 − 1/p 2 = β/n, 1 < p 1 < ∞, 0 ⩽ β < n. Furthermore, the characterization of on the homogenous Herz space (ℝ n ) was obtained. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10571014, 10371080) and the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No. 20040027001) |
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Keywords: | n-dimensional fractional Hardy operator commutator CṀ O function homogeneous Herz space |
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