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Commutators of BMO functions and singular integral operators with non-smooth kernels. (English) Zbl 1023.42010
Summary: Let 𝒳 be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on L p (𝒳) for some p, 1<p<. We give a sufficient condition on the kernel of T so that if a function bBMO(𝒳), then the commutator [b,T]=T(bf)-bT(f) is bounded on L p spaces for all p, 1<p<. Our condition is weaker than the usual Hörmander condition. Application include L p -boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.

42B20Singular and oscillatory integrals, several variables
47G10Integral operators
43A85Analysis on homogeneous spaces