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

Published online by Cambridge University Press:  17 April 2009

Xuan Thinh Duong  and
Lixin Yan
Xuan Thinh Duong
Affiliation:
Department of Mathematics, Macquarie University, New South Wales 2109, Australia e-mail: [email protected]
Lixin Yan
Affiliation:
Department of Mathematics, Macquarie University, New South Wales 2109, Australia e-mail: [email protected] and Department of Mathematics, Zhongshan University Guangzhou 510275, Peoples Republic of China
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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 ∈ 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 187 - 200
Copyright
Copyright © Australian Mathematical Society 2003

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