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In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let w⃗=(w_1,...,w_m) and ν = w_1^1/m...w_m^1/m, the main result of the paper sentences that under different conditions on the weights we can obtain T(f⃗ )(x)/v_L^1/m, ∞(ν v^1/m)≤ C ∏_i=1^mf_i_L^1(w_i), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M,doi:10.4064/sm170529-31-8 fatcat:tgryz46zjfddpeddgqsamqkrs4