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.
Original language | English |
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Pages (from-to) | 187-200 |
Number of pages | 14 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 67 |
Issue number | 2 |
Publication status | Published - Apr 2003 |