Zhou, Jiang; Ma, Bolin Marcinkiewicz commutators with Lipschitz functions in non-homogeneous spaces. (English) Zbl 1266.42051 Can. Math. Bull. 55, No. 3, 646-662 (2012). 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.” Reviewer: Hussain Al-Qassem (Doha) Cited in 4 Documents 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 Keywords:non doubling measure; Marcinkiewicz integral; commutator; Lip\(_{\beta}(\mu), H^1(\mu)\) PDFBibTeX XMLCite \textit{J. Zhou} and \textit{B. Ma}, Can. Math. Bull. 55, No. 3, 646--662 (2012; Zbl 1266.42051) Full Text: DOI