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| In this paper, we consider the boundedness and compactness of the multilinear singular integral operator on Morrey spaces, which is defined by\begin{align*}T_Af(x)={\rm{p.v.}}\int_{\mathbb{R}^n} \frac{\Omega(x-y)}{|x-y|^{n+1}} R(A;x,y)f(y)dy,\end{align*}where $R(A;x,y)=A(x)-A(y)-\nabla A(y)\cdot(x-y)$ with $D^\beta A\in BMO(\mathbb{R}^n)$ for all $|\beta|=1$.We prove that $T_A$ is bounded and compact on Morrey spaces $L^{p,\lambda}(\mathbb{R}^n)$ for all $1<p<\infty$ with $\Omega$ and $A$ satisfying some conditions. Moreover, the boundedness and compactness of the maximal multilinear singular integral operator $T_{A,*}$ on Morrey spaces are also given in this paper. |
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| Keywords:multilinear operator, compactness, rough kernel, Morrey space |
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