Multilinear Singular Integrals and their Commutators with Nonsmooth Kernels on Weighted Morrey Spaces

Abstract

Some multilinear maximal functions and the generalized Calderón-Zygmund operators and their commutators with nonsmooth kernels are studied. The purpose of this paper is to establish that these operators are bounded on certain product Morrey spaces $L^{p,k}({ℝ}^n)$. Based on the boundedness of these operators from $L^{p_{\mathrm{1}}}({\omega }_i)\times \cdots \times L^{p_m}({\omega }_m)$ to $L^p({\prod }_{j=\mathrm{1}}^m\mathrm{‍}{\omega }_j^{p/p_j})$, we obtained that they are also bounded from $L^{p_{\mathrm{1}},k}({\omega }_i)\times \cdots \times L^{p_m,k}({\omega }_m)$ to $L^{p,k}({\prod }_{j=\mathrm{1}}^m\mathrm{‍}{\omega }_j^{p/p_j})$ with , , $\mathrm{1}/p=\mathrm{1}/p_{\mathrm{1}},\dots ,p_m$ and ${\omega }_j\in A_{p_j}$, $j=\mathrm{1},\dots ,m$.