A WEIGHTED COMPACTNESS CRITERION FOR COMMUTATORS ASSOCIATED WITH GENERALIZED CALDERON-ZYGMUND OPERATORS

Let T be a bounded operator on L-p( R-n). Under the assumption that the kernel of T satisfies some Hormander-type estimates, we obtain a boundedness criterion for the multilinear commutators T-(b) over right arrow on the weighted Lebesgue spaces L-p(omega) with (b) over right arrow is an element of BMO(R-n) and omega belonging to the Muckenhoupt weight class A(p/ m'). Further, for (b) over right arrow is an element of CMO(R-n), the vanishing mean oscillation space, a criterion of L-p-weighted compactness of T-(b) over right arrow is established. As applications, the weighted L-p-boundedness and L-p-compactness criteria can be applied to the theta-type Calderon-Zygmund operator and its commutators.