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Volume 31, Issue 1
Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

S. P. Tao & L. J. Wang

Anal. Theory Appl., 31 (2015), pp. 13-24.

Published online: 2017-01

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  • 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.

  • AMS Subject Headings

42B20, 42B25, 42B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-13, author = {S. P. Tao and L. J. Wang}, title = {Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {1}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n1.2}, url = {http://global-sci.org/intro/article_detail/ata/4619.html} }
TY - JOUR T1 - Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent AU - S. P. Tao & L. J. Wang JO - Analysis in Theory and Applications VL - 1 SP - 13 EP - 24 PY - 2017 DA - 2017/01 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n1.2 UR - https://global-sci.org/intro/article_detail/ata/4619.html KW - Parameterized Littlewood-Paley operators, commutators, Lebesgue spaces with variable exponent. AB -

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.

S. P. Tao and L. J. Wang. (2017). Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent. Analysis in Theory and Applications. 31 (1). 13-24. doi:10.4208/ata.2015.v31.n1.2
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