Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fefferman-Stein inequalities for the Hardy-Littlewood maximal function
  on the infinite rooted $k$-ary tree   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 \[ w\left(\left\{ x\in
T\,:\,Mf(x)>\lambda\right\} \right)\leq
c_{s}\frac{1}{\lambda}\int_{T}|f(x)|M(w^{s})(x)^{\frac{1}{s}}dx\qquad s>1 \] 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.

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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th