Multilinear fractional Calder\'{o}n-Zygmund operators with Dini type kernel

In this paper, the main purpose is to consider a number of results concerning boundedness of multilinear fractional Calder\'{o}n-Zygmund operators with kernels of mild regularity. Let $T_{\alpha}$ be a multilinear fractional Calder\'{o}n-Zygmund operators of type $\omega(t)$ with $\omega$ being nondecreasing and $\omega \in \text{Dini}(1)$. The end-point weak-type estimates for multilinear operator $T_{\alpha}$ are obtained. Moreover, some boundedness properties of the multilinear fractional operators are also established on variable exponent Lebesgue spaces.