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| In this paper, we discuss the $L^p$ compactness of Calder'on type commutators $T_A$ defined byegin{align*}T_Af(x)={
m p.v.}int_{R^n} rac{Omega(x-y)}{|x-y|^{n+1}} R(A;x,y)f(y)dy,end{align*}where $R(A;x,y)=A(x)-A(y)-
abla A(y)cdot(x-y)$ with $D^eta Ain BMO(R^n)$ for all $nge 2$ and $|eta|=1$, and $Omega$ is homogeneous of degree zero and has a vanishing moment of order one on $mathbb{S}^{n-1}$.We prove that both of $T_A$ and its maximal operator $T_{A,*}$ are compact operators on $L^p(R^n)$ for all $1<p<infty$ with $A$ satisfying some conditions. Moreover, the compactness of the fractional operators $I_{lpha,A,m}$ and $M_{lpha,A,m}$ are also given. |
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| Keywords:Calder'on type commutator, maximal operator, fractional integral operators, compactness |
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