Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic decompositions, two stars theorems, and distances for the
  Bourgain-Brezis-Mironescu space and other big spaces   Given a Banach space $E$ with a supremum-type norm induced by a collection of
operators, we prove that $E$ is a dual space and provide an atomic
decomposition of its predual. We apply this result, and some results obtained
previously by one of the authors, to the function space $\mathcal{B}$
introduced recently by Bourgain, Brezis, and Mironescu. This yields an atomic
decomposition of the predual $\mathcal{B}_\ast$, the biduality result that
$\mathcal{B}_0^\ast = \mathcal{B}_\ast$ and $\mathcal{B}_\ast^\ast =
\mathcal{B}$, and a formula for the distance from an element $f \in
\mathcal{B}$ to $\mathcal{B}_0$.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin