论文标题
Fefferman-Stein的不平等现象，用于无限生根$ k $ ary树上强硬木的最大功能
Fefferman-Stein inequalities for the Hardy-Littlewood maximal function on the infinite rooted $k$-ary tree
论文作者
论文摘要
在本文中，提供了{无限生根} $ k $ -ary树上强硬木材最大功能的加权端点估计。由Naor和Tao激励以下Fefferman-Stein估计\ [w \ left（\ left \ {x \ in t \，：\，mf（x）>λ\ right \ right \} \ right）\ leq c_{s}\frac{1}λ\int_{T}|f(x)|M(w^{s})(x)^{\frac{1}{s}}dx\qquad s>1 \] is settled and moreover it {is shown it} is sharp, in the sense that it does not hold in general if $s=1$.一些非琐碎权重的例子，以便提供了加权弱$（1,1）$估计的估计。 {强} fefferman-stein类型估计，因此获得了一些矢量值的扩展。在附录中，建立了Soria和Tradacete在无限树上的摘要{定理}的加权对应物。
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 \[ w\left(\left\{ x\in T\,:\,Mf(x)>λ\right\} \right)\leq c_{s}\frac{1}λ\int_{T}|f(x)|M(w^{s})(x)^{\frac{1}{s}}dx\qquad s>1 \] 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.
