JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2023.477

    Next Articles

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

PDF (PC)

130

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

CLC Number: 

  • 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.
[1] Zhanhong LIU,Shuangping TAO. Weighted estimates of fractional maximal operator and its commutator on Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 108-115.
[2] LIU Ming, TAO Shuang-ping. Boundedness of fractional maximal operator on generalized Orlicz-Morrey spaces of homogeneous type [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 22-31.
[3] TAO Shuang-ping, YANG Yu-he. Weighted estimates of fractional maximal operator and its commutator on weighted λ-central Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 68-75.
[4] TAO Shuang-ping, GAO Rong. Estimates of multilinear fractional integrals and maximal operators on weighted Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 30-37.
[5] SUN Ai-wen, WANG Xiao-shan, SHU Li-sheng. Boundedness of the Littlewood-Paley function g*λ, μ  on the generalized
Morrey spaces with non-doubling measures [J]. J4, 2013, 48(12): 96-99.
[6] GENG Su-li, ZHAO Kai*, ZHANG Li-ping. Boundedness of Littlewood-Paley operators with non-doubling measures [J]. J4, 2013, 48(10): 78-81.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd