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 - <p style="text-align: justify;">In this paper, it is proved that the commutator&nbsp;$\mathcal{H}_{β,b}$ 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 $0&lt;α&lt;1,1&lt;p, q&lt;∞$ 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.</p>