Duality of weighted multiparameter Triebel-Lizorkin spaces

In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces ${\dot{F}}_p^{\alpha ,q}\left(\omega ;{\mathbb{R}}^{n_1}\times {\mathbb{R}}^{n_2}\right)$ based on the Frazier and Jawerth' method in 11]. This space was firstly introduced in 18]. Then we establish its dual space and get that ${\left({\dot{F}}_p^{\alpha ,q}\right)}^{*}={\text{CMO}}_p^{-\alpha ,q\text{'}}$ for 0 < p ≤ 1.