Bulletin of the Australian Mathematical Society

Research Article

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

Xuan Thinh Duonga1 and Lixin Yana2

a1 Department of Mathematics, Macquarie University, New South Wales 2109, Australia e-mail: duong@ics.mq.edu.au

a2 Department of Mathematics, Macquarie University, New South Wales 2109, Australia e-mail: lixin@ics.mq.edu.au and Department of Mathematics, Zhongshan University Guangzhou 510275, Peoples Republic of China

Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on Lp (χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b xs2208 BMO(χ), the commutator [b, T](f) = T (bf) – bT (f) is bounded on Lp spaces for all p, 1 < p > ∞. Our condition is weaker than the usual Hörmander condition. Applications include Lp-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.

(Received May 30 2002)