Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic and molecular decompositions in variable exponent 2-microlocal
  spaces and applications   In this article we study atomic and molecular decompositions in
$2$-microlocal Besov and Triebel--Lizorkin spaces with variable integrability.
We show that, in most cases, the convergence implied in such decompositions
holds not only in the distributions sense, but also in the function spaces
themselves. As an application, we give a simple proof for the denseness of the
Schwartz class in such spaces. Some other properties, like Sobolev embeddings,
are also obtained via atomic representations.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
1
The categories of this paper are: cs