Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The equivalence between pointwise Hardy inequalities and uniform fatness   We prove an equivalence result between the validity of a pointwise Hardy
inequality in a domain and uniform capacity density of the complement. This
result is new even in Euclidean spaces, but our methods apply in general metric
spaces as well. We also present a new transparent proof for the fact that
uniform capacity density implies the classical integral version of the Hardy
inequality in the setting of metric spaces. In addition, we consider the
relations between the above concepts and certain Hausdorff content conditions.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an