- Turkish Journal of Mathematics
- Vol: 40 Issue: 1
- Parameterized Littlewood--Paley operators and their commutators on Herz spaces with variable exponen...
Parameterized Littlewood--Paley operators and their commutators on Herz spaces with variable exponents
Authors : Lijuan Wang, Shuangping Tao
Pages : 122-145
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Parameterized Littlewood--Paley operators, commutators, Herz spaces with variable exponent, BMO spaces, Lipschitz spaces