分数次极大奇异积分交换子的点态估计及其应用

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1024-1036.

分数次极大奇异积分交换子的点态估计及其应用

杨雪纯(),李宝德^*()

新疆大学数学与系统科学学院乌鲁木齐 830017

收稿日期:2022-08-08 修回日期:2022-11-05 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 李宝德 E-mail:2760978447@qq.com;baodeli@xju.edu.cn
作者简介:杨雪纯，E-mail: 2760978447@qq.com
基金资助:
国家自然科学基金(12261083);国家自然科学基金(12161083);新疆自然科学基金(2020D01C048)

Pointwise Estimate of Fractional Maximal Singular Integral Commutators and its Application

Yang Xuechun(),Li Baode^*()

College of Mathematics and System Science, Xinjiang University, Urumqi 830017

Received:2022-08-08 Revised:2022-11-05 Online:2023-08-26 Published:2023-07-03
Contact: Baode Li E-mail:2760978447@qq.com;baodeli@xju.edu.cn
Supported by:
NSFC(12261083);NSFC(12161083);Natural Science Foundation of Xinjiang Uyghur Autonomous Region(2020D01C048)

摘要/Abstract

摘要：

该文引入了一类与变指标利普希茨函数相关的分数次极大奇异积分交换子, 其中变指标利普希茨函数是 $BMO$ 函数和经典利普希茨函数的推广. 然后该文得到了此交换子的点态估计. 作为应用, 该文得到了此交换子在变指标勒贝格空间上的有界性, 上述结果在常指标情形下也是新的.

关键词: 利普希茨函数, 分数次奇异积分, 交换子

Abstract:

In this paper, we introduce a class of fractional maximal singular integral commutators related to variable Lipschitz functions, which is a generalization of $BMO$ functions and classical Lipschitz functions. Then we obtain a pointwise estimate of this commutator. As an application, we obtain the boundedness of this commutator in variable Lebesgue spaces. The above results are also new even in the constant exponent context.

Key words: Lipschitz function, Fractional singular integral, Commutator

中图分类号:

O174.1

杨雪纯,李宝德. 分数次极大奇异积分交换子的点态估计及其应用[J]. 数学物理学报, 2023, 43(4): 1024-1036.

Yang Xuechun,Li Baode. Pointwise Estimate of Fractional Maximal Singular Integral Commutators and its Application[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1024-1036.

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