TY - JOUR
T1 - Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent
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 - <p style="text-align: justify;">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.</p>