Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension-free estimates for discrete Hardy-Littlewood averaging
  operators over the cubes in $\mathbb Z^d$   Dimension-free bounds will be provided in maximal and $r$-variational
inequalities on $\ell^p(\mathbb Z^d)$ corresponding to the discrete
Hardy-Littlewood averaging operators defined over the cubes in $\mathbb Z^d$.
We will also construct an example of a symmetric convex body in $\mathbb Z^d$
for which maximal dimension-free bounds fail on $\ell^p(\mathbb Z^d)$ for all
$p\in(1, \infty)$. Finally, some applications in ergodic theory will be
discussed.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex