The compactness of commutators of Calder\'on-Zgymund operators with Dini condition

Let $T$ be the $\theta$-type Calder\'on-Zgymund operator with Dini condition. In this paper, we prove that for $b\in {\rm CMO}(\mathbb R^n)$, the commutator generated by $T$ with $b$ and the corresponding maximal commutator, are both compact operators on $L^{p}(\omega)$ spaces, where $\omega$ be the Muchenhoupt $A_p$ weight function and $1<p<\infty$.