Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent
Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 13–24
Abstract
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Littlewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley $g_{\lambda}^{\ast}$-functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n1.2
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 13–24
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Parameterized Littlewood-Paley operators commutators Lebesgue spaces with variable exponent.
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