具有可变光滑指标的弱 Musielak-Orlicz-Triebel-Lizorkin 空间

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 687-701.

具有可变光滑指标的弱 Musielak-Orlicz-Triebel-Lizorkin 空间

代玉娇¹(),徐景实^1,^2,^3,^*()

¹桂林电子科技大学数学与计算科学学院广西桂林 541004
²广西应用数学中心广西桂林 541004
³广西高校数据分析与计算重点实验室广西桂林 541004

收稿日期:2024-05-25 修回日期:2024-12-10 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *徐景实, E-mail:jingshixu@126.com
作者简介:代玉娇, E-mail: 484612643@qq.com
基金资助:
国家自然科学基金(12161022);广西科学与技术项目(Guike AD23023002)

Weak Musicelak-Orlicz-Triebel-Lizorkin Spaces with Variable Smooth Exponent

Dai Yujiao¹(),Xu Jingshi^1,^2,^3,^*()

¹School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi Guilin 541004
²Center for Applied Mathematics of Guangxi (GUET), Guangxi Guilin 541004
³Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Guilin 541004

Received:2024-05-25 Revised:2024-12-10 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12161022);Science and Technology Project of Guangxi(Guike AD23023002)

摘要/Abstract

摘要：

首次引入具有可变光滑指标的弱 Musielak-Orlicz- Triebel-Lizorkin 空间. 然后, 建立弱 Musielak-Orlicz 空间的一个向量值估计. 作为应用, 借助于 Peetre 极大函数给出这些空间的等价拟范数. 最后, 得到这些新空间上 $ \varphi $ 变换的有界性及其原子和分子分解.

关键词: 可变光滑指标, 弱 Musielak-Orlicz 空间, Triebel-Lizorkin 空间, 原子, 分子, 极大函数

Abstract:

Weak Musielak-Orlicz-Triebel-Lizorkin spaces with variable smooth exponent are first introduced. Then we establish a vector estimate for weak Musielak-Orlicz spaces. As an application we give equivalent quasi-norms in these new spaces by means of Peetre 's maximal functions. Finally, we obtain the boundedness of the $ \varphi $ transform on these new spaces and their atomic and molecular decompositions.

Key words: variable smooth exponent, weak Musielak-Orlicz space, triebel-Lizorkin space, atom, molecule, maximal function

中图分类号:

O177.1

代玉娇, 徐景实. 具有可变光滑指标的弱 Musielak-Orlicz-Triebel-Lizorkin 空间[J]. 数学物理学报, 2025, 45(3): 687-701.

Dai Yujiao, Xu Jingshi. Weak Musicelak-Orlicz-Triebel-Lizorkin Spaces with Variable Smooth Exponent[J]. Acta mathematica scientia,Series A, 2025, 45(3): 687-701.

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