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Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces
  Published:2011-07-04
 Printed: Sep 2012
Canadian Mathematical Bulletin
  • Jiang Zhou,
    College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. China
  • Bolin Ma,
    College of Mathematics and Econometrics, Hunan University, ChangSha, 410082, P.R. China
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Abstract

Under the assumption that $\mu$ is a nondoubling measure, we study certain commutators generated by the Lipschitz function and the 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.
Keywords: non doubling measure, Marcinkiewicz integral, commutator, ${\rm Lip}_{\beta}(\mu)$, $H^1(\mu)$ non doubling measure, Marcinkiewicz integral, commutator, ${\rm Lip}_{\beta}(\mu)$, $H^1(\mu)$
MSC Classifications: 42B25, 47B47, 42B20, 47A30 show english descriptions Maximal functions, Littlewood-Paley theory
Commutators, derivations, elementary operators, etc.
Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Norms (inequalities, more than one norm, etc.) 42B25 - Maximal functions, Littlewood-Paley theory
47B47 - Commutators, derivations, elementary operators, etc.
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
47A30 - Norms (inequalities, more than one norm, etc.)
 
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