TY - JOUR T1 - Weighted Boundedness of Commutators of Generalized Calderόn-Zygmund Operators JO - Analysis in Theory and Applications VL - 3 SP - 209 EP - 224 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2017-0050 UR - https://global-sci.org/intro/article_detail/ata/12836.html KW - Commutator, Lipschitz function, weighted hardy space, Herz space. AB -

$[b,T]$ denotes the commutator of generalized Calderón-Zygmund operators $T$ with Lipschitz function $b$, where $b ∈ \rm{Lip}_β(R^n)$, $(0<β≤1)$ and $T$ is a $θ(t)$−type Calderón-Zygmund operator. The commutator $[b,T]$ generated by $b$ and $T$ is defined by 

$$[b,T] f(x)=b(x)Tf(x)−T(bf)(x)=∫k(x,y)(b(x)−b(y))f(y)dy.$$

In this paper, the authors discuss the boundedness of the commutator $[b,T]$ on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that $[b,T]$ is bounded from $H^p(ω^p)$ to $L^q(ω^q)$, and from $H\dot{K}^{α,p}_{q_1}(ω_1,ω^{q_1}_2)$ to $\dot{K}^{α,p}_{q_2}(ω_1,ω^{q_2}_2)$. The results extend and generalize the well-known ones in [7].