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

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.