Boundedness for Multilinear Commutators of Littlewood-Paley Operator

Abstract

In this paper, boundedness for the multilinear commutators of Littlewood-Paley operator is considered. We prove that the multilinear commutators $g_{\psi,\vec{b}}$ generated by Littlewood-Paley operator and Lipschitz function is bounded from $L^{p}({ R}^{n})$ into $\dot{\wedge}_{(\beta-\frac{n}{p})}({ R}^{n})$ and from $L^{\frac{n}{\beta}}({ R}^{n})$ into BMO$({ R}^{n})$.