Turkish Journal of Mathematics
Abstract
The aim of this paper is to deal with Littlewood--Paley operators with real parameters, including the parameterized Lusin area integrals and the parameterized Littlewood--Paley $g_{\lambda}^{\ast}$-functions, and their commutators on Herz spaces with two variable exponents $p(\cdot),~q(\cdot)$. By using the properties of the Lebesgue spaces with variable exponents, the boundedness of the parameterized Littlewood--Paley operators and their commutators generated respectively by BMO function and Lipschitz function is obtained on those Herz spaces.
DOI
10.3906/mat-1412-52
Keywords
Parameterized Littlewood--Paley operators, commutators, Herz spaces with variable exponent, BMO spaces, Lipschitz spaces
First Page
122
Last Page
145
Recommended Citation
WANG, L, & TAO, S (2016). Parameterized Littlewood--Paley operators and their commutators on Herz spaces with variable exponents. Turkish Journal of Mathematics 40 (1): 122-145. https://doi.org/10.3906/mat-1412-52
