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Volume 25, Issue 3
Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators

Qingyu Zheng & Zunwei Fu

Commun. Math. Res., 25 (2009), pp. 241-245.

Published online: 2021-07

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  • 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.

  • Keywords

commutator, $n$-dimensional fractional Hardy operator, Lipschitz function. Herz space.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-241, author = {Qingyu and Zheng and and 18151 and and Qingyu Zheng and Zunwei and Fu and and 18152 and and Zunwei Fu}, title = {Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {3}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19331.html} }
TY - JOUR T1 - Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators AU - Zheng , Qingyu AU - Fu , Zunwei JO - Communications in Mathematical Research VL - 3 SP - 241 EP - 245 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19331.html KW - commutator, $n$-dimensional fractional Hardy operator, Lipschitz function. Herz space. AB -

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.

QingyuZheng & ZunweiFu. (2021). Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators. Communications in Mathematical Research . 25 (3). 241-245. doi:
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