Characterization for commutators of <i>n</i> -dimensional fractional Hardy operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Characterization for commutators of n -dimensional fractional Hardy operators

Authors:	Zun-wei Fu Zong-guang Liu Shan-zhen Lu Hong-bin Wang

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

Abstract:	In this paper, it was proved that the commutator $mathcal{H}_{beta ,b}$ generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L ^p1 (ℝⁿ) to L ^p2 (ℝⁿ) if and only if b is a CṀO(ℝⁿ) function, where 1/p ₁ − 1/p ₂ = β/n, 1 < p ₁ < ∞, 0 ⩽ β < n. Furthermore, the characterization of $mathcal{H}_{beta ,b}$ on the homogenous Herz space $dot K_q^{alpha ,p}$ (ℝⁿ) 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)

Keywords:	n-dimensional fractional Hardy operator commutator CṀ O function homogeneous Herz space
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