Boundedness for multilinear commutator of Littlewood–Paley operator on Hardy and Herz–Hardy spaces

In this paper, the $(H^p_{\vec{b}},L^p)$ and $(H\dot{K}^{\alpha,p}_{q,\vec{b}},\dot{K}_q^{\alpha,p})$ type boundedness for the multilinear commutator associated with the Littlewood–Paley operator are obtained.