Geodesic
Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 646-662

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DOI

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.
DOI : 10.4153/CMB-2011-139-1
Mots-clés : 42B25, 47B47, 42B20, 47A30, non doubling measure, Marcinkiewicz integral, commutator, Lipβ (μ), H 1(μ) 
Zhou, Jiang; Ma, Bolin. Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 646-662. doi: 10.4153/CMB-2011-139-1
@article{10_4153_CMB_2011_139_1,
     author = {Zhou, Jiang and Ma, Bolin},
     title = {Marcinkiewicz {Commutators} with {Lipschitz} {Functions} in {Non-homogeneous} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {646--662},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-139-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-139-1/}
}
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