Parameterized Littlewood--Paley operators and their commutators on Herz spaces with variable exponents

Authors

Lijuan WANG
SHUANGPING TAO

DOI

10.3906/mat-1412-52

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

First Page

122

Last Page

145

Recommended Citation

WANG, Lijuan and TAO, SHUANGPING (2016) "Parameterized Littlewood--Paley operators and their commutators on Herz spaces with variable exponents," Turkish Journal of Mathematics: Vol. 40: No. 1, Article 12. https://doi.org/10.3906/mat-1412-52
Available at: https://journals.tubitak.gov.tr/math/vol40/iss1/12