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The main purpose of this paper is to prove that the boundedness of the commutator [...] Mκ,b∗ ${ℳ}_{\kappa ,b}^{*}$ generated by the Littlewood-Paley operator [...] Mκ∗ ${ℳ}_{\kappa }^{*}$ and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of [...] Mκ∗ ${ℳ}_{\kappa }^{*}$ satisfies a certain Hörmander-type condition, the authors prove that [...] Mκ,b∗ ${ℳ}_{\kappa ,b}^{*}$ is bounded on Lebesgue spaces Lp(μ) for 1 < p < ∞, bounded from the space...

We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators.