Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple proof of the Hardy inequality on Carnot groups and for some
  hypoelliptic families of vector fields   We give an elementary proof of the classical Hardy inequality on any Carnot
group, using only integration by parts and a fine analysis of the commutator
structure, which was not deemed possible until now. We also discuss the
conditions under which this technique can be generalized to deal with
hypoelliptic families of vector fields, which, in this case, leads to an open
problem regarding the symbol properties of the gauge norm.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph