Let ( 𝒳 , d , μ ) $({\mathcal {X}},d,\mu )$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. Under this assumption, the authors establish some weighted norm inequalities for the multilinear Calderón–Zygmund operators via first obtaining some weighted estimates involving the John–Strömberg maximal operators and the John–Strömberg sharp maximal operators.

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: In this paper, we consider a kind of multilinear operators related to oscillatory singular integrals with rough kernels and give a criterion of certain boundedness for this kind of operators.