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Ombrosi, Sheldy J. Rivera Ríos, Israel P. Safe, Martín D. 2024-12-03T08:12:29Z 2024-12-03T08:12:29Z 2020-08-27 Sheldy Ombrosi, Israel P Rivera-Ríos, Martín D Safe, Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree, International Mathematics Research Notices, Volume 2021, Issue 4, February 2021, Pages 2736–2762, https://doi.org/10.1093/imrn/rnaa220 https://hdl.handle.net/10630/35450 10.1093/imrn/rnaa220 In this paper weighted endpoint estimates for the Hardy-Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [23] the following Fefferman-Stein estimate w ({x ∈ T : Mf(x) > λ}) ≤ cs 1 λ Z T |f(x)|M(w s )(x) 1 s dx s > 1 is settled and moreover it is shown it is sharp, in the sense that it does not hold in general if s = 1. Some examples of non trivial weights such that the weighted weak type (1, 1) estimate holds are provided. A strong Fefferman-Stein type estimate and as a consequence some vector valued extensions are obtained. In the Appendix a weighted counterpart of the abstract theorem of Soria and Tradacete on infinite trees [38] is established. eng open access Análisis matemático Desigualdades (Matemáticas) Fefferman-Stein inequalities for the Hardy-Littlewood maximal function on the infinite rooted k-ary tree. journal article