Boundedness for the multilinear commutator associated with the Littlewood-paley operator on two 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 on Hardy and Herz-Hardy Spaces are obtained, using some techniques for classical inequalities