Year: 2009
Author: Qingyu Zheng, Zunwei Fu
Communications in Mathematical Research , Vol. 25 (2009), Iss. 3 : pp. 241–245
Abstract
In this paper, it is proved that the commutator $\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0<α<1,1<p, q<∞$ and $1/p-1/q=(α+β)/n$. Furthermore, the boundedness of $\mathcal{H}_{β,b}$ on the homogenous Herz space $\dot{K}_q^{α,p}(\mathbb{R}^n)$ is obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CMR-19331
Communications in Mathematical Research , Vol. 25 (2009), Iss. 3 : pp. 241–245
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 5
Keywords: commutator $n$-dimensional fractional Hardy operator Lipschitz function. Herz space.