WEAK TYPE ENDPOINT ESTIMATES FOR THE COMMUTATORS OF ROUGH SINGULAR INTEGRAL OPERATORS

Let Omega be homogeneous of degree zero and have mean value zero on the unit sphere, Sn-1,T-Omega To be the convolution singular integral operator with kernel Omega(x)/vertical bar x vertical bar(n) . For b is an element of BMO(R-n), let T-Omega,T-b be the commutator of T-Omega. In this paper, by establishing suitable sparse dominations, the authors establish some weak type endpoint estimates of LlogL type for T-Omega,T-b when Omega is an element of L-q(Sn-1) for some q is an element of (1, infinity].