Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newtonian Lorentz Metric Spaces   This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these
spaces are Banach. We also study the global p,q-capacity and the p,q-modulus of
families of rectifiable curves. Under some additional assumptions (that is, the
space carries a doubling measure and a weak Poincare inequality) and some
restrictions on q, we show that the Lipschitz functions are dense in those
spaces. Moreover, in the same setting we show that the p,q-capacity is Choquet
provided that q is strictly greater than 1. We also provide a counterexample to
the density result of Lipschitz functions in the Euclidean setting when q is
infinite.

3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn