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In this paper,a weak type(1,1)estimate is established for the higher order commutator introduced by Christ and Joume which is defined byT[a1,…,a1]f(x)=p.v∫R^dK(x-y)(lПi=1 mx,yai)·f(y)dy,where K is the standard Calderon-Zygmund convolution kernel on R