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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 Lp,k(ℝn). Based on the boundedness of these operators from Lp1(ωi)×⋯×Lpm(ωm) to Lp(∏j=1m‍ωjp/pj), we obtained that they are also bounded from Lp1,k(ωi)×⋯×Lpm,k(ωm) to Lp,k(∏j=1m‍ωjp/pj) with 0<k<1, 1<pj<∞, 1/p=1/p1,…,pm and ωj∈Apj, j=1,…,m

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