Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1013-1022.

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Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

冀蕾¹(),魏明权^2,^*(),燕敦验¹()

¹中国科学院大学数学科学学院北京 100049
²信阳师范大学数学与统计学院河南信阳 464000

收稿日期:2023-10-17 修回日期:2025-01-03 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: weimingquan11@mails.ucas.ac.cn
作者简介:E-mail: jilei21@mails.ucas.ac.cn;|ydunyan@ucas.ac.cn
基金资助:
国家自然科学基金(12271501);国家自然科学基金(12301123);国家自然科学基金(12071052);信阳师范大学 "南湖学者奖励计划"青年项目

Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces

Ji Lei¹(),Wei Mingquan^2,^*(),Yan Dunyan¹()

¹School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049
²School of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000

Received:2023-10-17 Revised:2025-01-03 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12271501);NSFC(12301123);NSFC(12071052);Nanhu Scholar Program for Young Scholars of Xinyang Normal University

摘要/Abstract

摘要：

该文给出了 $n$ 维 Hardy 型算子的交换子 $H_b$ 和 $H^*_b$ 从中心 Morrey 空间 $\dot{M}^{p,\lambda}(\mathbb{R}^n)$ 到弱中心 Morrey 空间 $W\dot{M}^{p,\lambda}(\mathbb{R}^n)$ 有界的一些刻画, 推广了 Lebesgue 空间上的相应结果.

关键词: $n$维 Hardy 型算子, 交换子, 弱中心 Morrey 空间, 弱中心有界平均振荡空间

Abstract:

We provide some characterizations of the boundedness for commutators of $n$-dimensional Hardy-type operators $H_b$ and $H^*_b$ from the central Morrey space $\dot{M}^{p,\lambda}(\mathbb{R}^n)$ to the weak central Morrey space $W\dot{M}^{p,\lambda}(\mathbb{R}^n)$, which extends the corresponding results on Lebesgue spaces.

Key words: $n$-dimensional Hardy-type operator, commutator, weak central Morrey space, weak central bounded mean oscillation space

中图分类号:

O174.2

冀蕾, 魏明权, 燕敦验. Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画[J]. 数学物理学报, 2025, 45(4): 1013-1022.

Ji Lei, Wei Mingquan, Yan Dunyan. Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1013-1022.

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Hardy 型算子的交换子在中心 Morrey 空间上的弱有界性刻画

Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces

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