Characterization of Lipschitz Space via the Commutators of Fractional Maximal Functions on Variable Lebesgue Spaces

被引：3

作者：

Yang, Xuechun ^{[1
]}

Yang, Zhenzhen ^{[2
]}

Li, Baode ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China

[2] YiLi Normal Univ, Coll Math & Stat, Yining 835000, Peoples R China

来源：

POTENTIAL ANALYSIS | 2024年 / 60卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Variable Lebesgue space; Lipschitz space; Maximal function; Fractional maximal function; Commutator; OPERATORS; POTENTIALS; EXPONENT; ORDER;

D O I：

10.1007/s11118-023-10067-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the variable Lebesgue spaces, where the symbols of the commutators belong to the variable Lipschitz space. A useful tool is that a symbol b belongs a variable Lipschitz space of pointwise type if and only if b belongs to a variable Lipschitz space of integral type under certain assumptions.

引用

页码：703 / 720

页数：18

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