Multilinear fractional Calderón-Zygmund operators with Dini type kernel

Abstract

In this paper, the main purpose is to consider a number of results concerning boundedness of multilinear fractional Calderón-Zygmund operators with kernels of mild regularity. Let $T_{\alpha }$ be a multilinear fractional Calderón-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.