Fefferman-Stein inequalities for the Hardy-Littlewood maximal function on the infinite rooted k-ary tree

2020/03/22 by Sheldy Ombrosi, Israel P. Rivera-Ríos, Ombrosi, Sheldy +4
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #math.CA #math.CO #math.FA #math.MG

paper · pdf · doi:10.48550/arxiv.2003.10034

21 pages

arxiv created 2020/03/23 · arxiv updated 2020/03/24

Abstract

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 the following Fefferman-Stein estimate w(\ x∈ T : Mf(x)>λ\ )≤ c_s\frac1λ∫_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 is established.

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