Multilinear singular integrals and their commutators with nonsmooth kernels on weighted Morrey spaces (Q2015306)

Summary: 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 \(L^{p,k}(\mathbb R^n)\). Based on the boundedness of these operators from \(L^{p_1}(\omega_1)\times\cdots\times L^{p_m}(\omega_m)\) to \(L^p(\prod^m_{j=1}\omega_j^{p/p_j})\), we obtained that they are also bounded from \(L^{p_1,k}(\omega_1)\times\cdots\times L^{p_m,k}(\omega_m)\) to \(L^{p,k}(\prod^m_{j=1}\omega_j^{p/p_j})\) with \(0<k<1\), \(1<p_j<\infty\), \(1/p=1/p_1+\dots +1/p_m\) and \(\omega_j \in A_{p_j}\), \(j=1,\dots,m\).