# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 38 (2009) pp.137-151

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### Abstract

In this paper, we establish the CMO estimate for the higher-order commutator of Carlderón-Zygmund singular integral with rough kernel. This estimate enables us to get the CMO estimates for the higher-order commutators of a class of Marcinkiewicz integral operators $\mu_\Omega$, $\mu_{\Omega,\lambda}^{\ast}$ and $\mu_{\Omega,S}$ with rough kernels, which are corresponding to the Littlewood-Paley $g$ function, Littlewood-Paley $g_{\lambda}^{\ast}$ function and the Lusin area integral, respectively.

MSC(Primary) 42B20 42B30, 42B35 Commutator, Carlderón-Zygmund singular integral, Marcinkiewicz integral, Littlewood–Paley operator, CMO function, Herz space.