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Marcinkiewicz commutators with Lipschitz functions in non-homogeneous spaces. (English) Zbl 1266.42051

Authors’ abstract: “Under the assumption that \(\mu\) is a nondoubling measure, we study certain commutators generated by a Lipschitz function and a Marcinkiewicz integral whose kernel satisfies a Hörmander-type condition. We establish the boundedness of these commutators on the Lebesgue spaces, Lipschitz spaces, and Hardy spaces. Our results are extensions of known theorems in the doubling case.”

MSC:

42B25 Maximal functions, Littlewood-Paley theory
47B47 Commutators, derivations, elementary operators, etc.
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
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