Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension-Free $L^p$-Maximal Inequalities in $\mathbb{Z}_{m+1}^N$   For $m \geq 2$, let $(\mathbb{Z}_{m+1}^N, |\cdot|)$ denote the group equipped
with the so-called $l^0$ metric,
  \[ |y| = \left| \big( y(1), \dots, y(N) \big) \right| := | \{1 \leq i \leq N
: y(i) \neq 0 \} |,\] and define the $L^1$-normalized indicator of the
$r$-sphere, \[ \sigma_r := \frac{1}{|\{|x| = r\}|} 1_{\{|x| =r\}}.\] We study
the $L^p \to L^p$ mapping properties of the maximal operator \[ M^{N} f (x) :=
\sup_{r \leq N} | \sigma_r*f| \] acting on functions defined on
$\mathbb{Z}_{m+1}^N$.
  Specifically, we prove that for all $p>1$, there exist absolute constants
$C_{m,p}$ so that \[ \| M^{N} f \|_{L^p(\mathbb{Z}_{m+1}^N)} \leq C_{m,p} \| f
\|_{L^p(\mathbb{Z}_{m+1}^N)} \] for all $N$.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin