Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

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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