COMMUTATORS OF BMO FUNCTIONS AND SINGULAR INTEGRAL OPERATORS WITH NON-SMOOTH KERNELS ON SPACES OF HOMOGENEOUS TYPE OF FINITE MEASURE

摘要

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L~p (X), 1 < p < ∞. We give a sufficient condition on the kernel k(x,y) of T so that when a function b ∈ BMO (X) ,the commutator [b,T] (f) = T (bf) - bT (f) is bounded on spaces L~p for all p, 1 < p < ∞.