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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2023.477

• •    

齐次树上关于倍测度的分数次极大算子的有界性

叶晓峰,熊守龙,姜智聪   

  1. 华东交通大学理学院, 江西 南昌 330013
  • 发布日期:2025-07-25
  • 作者简介:叶晓峰(1980— ),男,副教授,博士,研究方向为调和分析. E-mail:xiaofye@163.com
  • 基金资助:
    国家自然科学基金资助项目(11661035)

Boundedness of fractional maximal operators with doubling measure on homogeneous trees

YE Xiaofeng, XIONG Shoulong, JIANG Zhicong   

  1. School of Science, East China Jiaotong University, Nanchang 330013, Jiangxi, China
  • Published:2025-07-25

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摘要： 定义分数次极大算子,并找到它的一个与极大算子相关的控制函数,由极大算子的弱(1,1)型得到分数次极大算子在齐次树上的有界性。

关键词: 齐次树, 分数次极大算子, 倍测度

Abstract: We defined the fractional maximal operators and found a control function related to the maximal operators. We obtain the boundedness of fractional maximal operators on homogeneous trees from the weak(1,1)type of maximal operators.

Key words: homogeneous trees, fractional maximal operator, doubling measure

中图分类号: 

  • O177
[1] DE MARI F, MONTI M, VALLARINO M. Harmonic Bergman projectors on homogeneous trees[J]. Potential Analysis, 2024, 61:153-182.
[2] MONTI M. H 1and BMO spaces for exponentially decreasing measures on homogeneous trees[EB/OL].(2023-01-18)[2024-07-03]. https://doi.org/10.48550/arXiv.2301.07600.
[3] HARDY G H, LITTLEWOOD J E. A maximal theorem with function-theoretic applications[J]. Acta Mathematica, 1930, 54(1):81-116.
[4] COIFMAN R R, WEISS G. Extensions of Hardy spaces and their use in analysis[J]. Bulletin of the American Mathematical Society, 1977, 83(4):569-645.
[5] LEVI M, SANTAGATI F. Hardy-Littlewood fractional maximal operators on homogeneous trees[EB/OL].(2022-11-21)[2024-07-03]. https://doi.org/10.48550/arXiv.2211.11871.
[6] CARBONARO A, MAUCERI G, MEDA S. H 1 and BMO for certain locally doubling metric measure spaces[J]. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2009, 8(3):543-582.
[7] CARBONARO A, MAUCERI G, MEDA S. H 1 and BMO for certain nondoubling metric measure spaces[EB/OL].(2008-08-01)[2024-07-03]. https://doi.org/10.48550/arXiv.0808.0146.
[8] COWLING M, MEDA S, SETTI A. An overview of harmonic analysis on the group of isometries of a homogeneous tree[J]. Expositiones mathematicae, 1998, 16(5):385-423.
[9] ARDITTI L, TABACCO A, VALLARINO M. BMO spaces on weighted homogeneous trees[J]. The Journal of Geometric Analysis, 2021, 31(9):8832-8849.
[10] ARDITTI L. Analysis on weighted homogeneous trees[D]. Torino: Politecnico di Torino, 2018.
[11] LOFSTROM J B J, BERGH J. Interpolation spaces[EB/OL].(2020-02-01)[2024-07-03]. https://www.tesble.com/10.1007/978-3-642-66451-9.
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