  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.
