Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete maximal functions in higher dimensions and applications to
  ergodic theory   We establish a higher dimensional counterpart of Bourgain's pointwise ergodic
theorem along an arbitrary integer-valued polynomial mapping. We achieve this
by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and
$r>\max\{p, p/(p-1)\}$. Moreover, we obtain the estimates which are uniform in
the coefficients of a polynomial mapping of fixed degree.

29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess