Commutators of BMO functions and singular integral operators with non-smooth kernels

Source abstract

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.