Volume 37 • Number 3 • 2014   • Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals Jianglong Wu and Qingguo Liu Abstract. Let $\mu_{\Omega,\vec{b}}$ be the multilinear commutator generalized by $\mu_{\Omega}$, the $n$-dimensional Marcinkiewicz integral, with $Osc_{\exp L^{^{\tau}}}(R^{n})$ functions for $\tau\ge 1$, where $Osc_{\exp L^{^{\tau}}}(R^{n})$ is a space of Orlicz type satisfying that $Osc_{\exp L^{^{\tau}}}(R^{n})=BMO(R^{n})$ if $\tau=1$ and $Osc_{\exp L^{^{\tau}}}(R^{n})\subset BMO(R^{n})$ if $\tau>1$. The authors establish the weighted weak $L\log L$-type estimates for $\mu_{\Omega,\vec{b}}$ when $\Omega$ satisfies a kind of Dini conditions. 2010 Mathematics Subject Classification: 42B20, 42B25, 42B99 Full text: PDF