Weighted weak type (1,1) estimate for the Christ-Journé type commutator

Let K be the Calderón-Zygmund convolution kernel on R~d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R~d)by T_af(x)=p.v.∫_(R~d)K(x-y)m_x,y~a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2.