齐性群上加权Hardy算子及其交换子

doi:10.7523/j.ucas.2025.003

中国科学院大学学报

齐性群上加权Hardy算子及其交换子

曹纪龙¹, 何骞君², 燕敦验¹

¹中国科学院大学数学科学学院, 北京 100049;
²北京信息科技大学理学院, 北京 100192

收稿日期:2024-12-10 修回日期:2025-02-20

Weighted Hardy operator and its commutators on homogeneous groups^∗

CAO Jilong¹, HE Qianjun², YAN Dunyan^1†

¹School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
²School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

Received:2024-12-10 Revised:2025-02-20
Contact: ^†E-mail: ydunyan@ucas. ac. cn
Supported by:
^*National Natural Science Foundation of China (Nos.12071473,12071052 and 12271501) and The Young Backbone Teacher Support Plan of Beijing Information Science and Technology University (No. YBT202449)

摘要/Abstract

摘要： 介绍了齐性群上的加权Hardy算子,获得其在中心Morrey空间与中心BMO空间上的最佳有界性。另外,也得出在中心Morrey空间中加权Hardy算子交换子有界的充要条件。

关键词: 齐性群, 加权Hardy算子, 最佳有界, 中心Morrey空间, 中心BMO空间

Abstract: Let $ \mathbb{G}$ denote be a homogeneous group, the authors introduce a type of weighted Hardy operators on homogeneous group and obtain their sharp bounds on central Morrey spaces and λ-central BMO spaces in the setting of homogeneous group. In addition, the authors obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted Hardy operators (with symbols in central BMO space) are bounded on the central Morrey spaces in the setting of homogeneous group.

Key words: homogeneous group, weighted Hardy operators, sharp bounds, central Morrey spaces, central BMO spaces

中图分类号:

O177

曹纪龙, 何骞君, 燕敦验. 齐性群上加权Hardy算子及其交换子[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2025.003.

CAO Jilong, HE Qianjun, YAN Dunyan. Weighted Hardy operator and its commutators on homogeneous groups^∗[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2025.003.

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