Weighted Hardy operator and its commutators on homogeneous groups∗

doi:10.7523/j.ucas.2025.003

Journal of University of Chinese Academy of Sciences

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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)

Abstract

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

CLC Number:

O177

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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Weighted Hardy operator and its commutators on homogeneous groups^∗

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