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Search: All articles in the CMB digital archive with keyword Marcinkiewicz integral

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1. CMB 2011 (vol 55 pp. 646)

Zhou, Jiang; Ma, Bolin
Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces
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, ${\rm Lip}_{\beta}(\mu)$, $H^1(\mu)$
Categories:42B25, 47B47, 42B20, 47A30

2. CMB 2010 (vol 54 pp. 100)

Fan, Dashan; Wu, Huoxiong
On the Generalized Marcinkiewicz Integral Operators with Rough Kernels
A class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on $L^p$ and Triebel--Lizorkin spaces is established.

Keywords: Marcinkiewicz integral, Littlewood--Paley theory, Triebel--Lizorkin space, rough kernel, product domain
Categories:42B20, , , , , 42B25, 42B30, 42B99

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