Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Hardy–Littlewood maximal operators on trees with bounded geometry
HTML articles powered by AMS MathViewer

by Matteo Levi, Stefano Meda, Federico Santagati and Maria Vallarino;
Trans. Amer. Math. Soc. 378 (2025), 3951-3979
DOI: https://doi.org/10.1090/tran/9229
Published electronically: March 19, 2025

Abstract:

In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy–Littlewood maximal operators on the class $\Upsilon _{a,b}$, $2\leq a\leq b$, of trees with $(a,b)$-bounded geometry. We find the sharp range of $p$, depending on $a$ and $b$, where the centred maximal operator is bounded on $L^p(\mathfrak {T})$ for all $\mathfrak {T}$ in $\Upsilon _{a,b}$. Precisely, the lower endpoint is $\log _a b$ if $b \leq a^2$ and $\infty$ otherwise. In particular, we show that if $b>a^2$, then there exists a tree in $\Upsilon _{a,b}$ for which the uncentred maximal function is bounded on $L^p$ if and only if $p=\infty$. We also extend these results to graphs which are strictly roughly isometric, in the sense of Kanai, to trees in the class $\Upsilon _{a,b}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 05C05, 43A99
  • Retrieve articles in all journals with MSC (2020): 05C05, 43A99
Bibliographic Information
  • Matteo Levi
  • Affiliation: Fac. de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain; and Dept. Matemàtica i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
  • MR Author ID: 1267296
  • ORCID: 0000-0002-6242-1770
  • Email: matteo.levi@ub.edu
  • Stefano Meda
  • Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via R. Cozzi 53, I-20125 Milano, Italy
  • MR Author ID: 122835
  • Email: stefano.meda@unimib.it
  • Federico Santagati
  • Affiliation: Dipartimento di Matematica, Dipartimento di Eccellenza 2023–2027; and Malga Center, Università di Genova, via Dodecaneso 35, Genova, Italy
  • MR Author ID: 1486817
  • ORCID: 0000-0003-4685-9956
  • Email: fedirico.santagati@edu.unige.it
  • Maria Vallarino
  • Affiliation: Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • MR Author ID: 787152
  • ORCID: 0000-0002-0023-9121
  • Email: maria.vallarino@polito.it
  • Received by editor(s): September 28, 2023
  • Received by editor(s) in revised form: April 18, 2024, and May 7, 2024
  • Published electronically: March 19, 2025
  • Additional Notes: The first, third, and fourth authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The first, third, and fourth authors were supported in part by the Project “Harmonic analysis on continuous and discrete structures” (bando Trapezio Compagnia di San Paolo CUP E13C21000270007). The first author was supported in part by the Generalitat de Catalunya (grant 2021 SGR 00071), the Spanish Ministerio de Ciencia e Innóvacion (project PID2021-12315NB-100).
  • Dedicated: This paper is dedicated to the memory of A. M.
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 3951-3979
  • MSC (2020): Primary 05C05, 43A99
  • DOI: https://doi.org/10.1090/tran/9229