Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on L p(χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b ∈ BMO(χ), the commutator [b,T](f) = T(bf) - bT(f) is bounded on L p spaces for all p, 1 < p < ∞. Our condition is weaker than the usual Hörmander condition. Applications include L p-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.
|Number of pages||14|
|Journal||Bulletin of the Australian Mathematical Society|
|Publication status||Published - Apr 2003|