Abstract In this paper, we use the discrete Littlewood–Paley–Stein analysis to get the duality result of the weighted product Hardy space for arbitrary number of parameters under a rather weak condition on the product weight w ∈ A ∞ ( ℝ n 1 × ⋯ × ℝ n k ) $w \in A_\infty ( {\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})$ . We will show that for any k ≥ 2, ( H w p ( ℝ n 1 × ⋯ × ℝ n k ) ) * = C M O w p ( ℝ n 1 × ⋯ × ℝ n k ) ${(H^p_w({\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k}))^\ast =\textup {CMO}^p_w({\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})}$ (a generalized Carleson measure), and obtain the boundedness of singular integral operators on BMO w $\mathrm {BMO}_w$ . Our theorems even when the weight function w = 1 extend the H 1-BMO duality of Chang–R. Fefferman for the non-weighted two-parameter Hardy space H 1 ( ℝ n × ℝ m ) $H^1({\mathbb {R}}^n\times {\mathbb {R}}^m)$ to H p ( ℝ n 1 × ⋯ × ℝ n k ) $H^p({\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})$ for all 0 < p ≤ 1 $0&lt;p\le 1$ and our weighted theory extends the duality result of Krug–Torchinsky on weighted Hardy spaces H w p ( ℝ n × ℝ m ) $H^p_w({\mathbb {R}}^n\times {\mathbb {R}}^m)$ for w ∈ A r ( ℝ n × ℝ m ) ${w\in A_r({\mathbb {R}}^n\times {\mathbb {R}}^m)}$ with 1 ≤ r ≤ 2 $1\le r\le 2$ and r / 2 < p ≤ 1 ${r/2&lt;p\le 1}$ to H w p ( ℝ n 1 × ⋯ × ℝ n k ) $H^p_w({\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})$ with w ∈ A ∞ ( ℝ n 1 × ⋯ × ℝ n k ) ${w \in A_\infty ( {\mathbb {R}}^{n_1} \times \cdots \times {\mathbb {R}}^{n_k})}$ for all 0 < p ≤ 1 ${0&lt;p\le 1}$ .