  We provide an intrinsic atomic characterization for 2-microlocal Besov and
Triebel-Lizorkin spaces with variable integrability on domains,
$B_{\p,\q}^{\bm{w}}(\Omega)$ and $F_{\p,\q}^{\bm{w}}(\Omega)$, where $\Omega$
is a regular domain. We use the already known decomposition with non-smooth
atoms for the spaces $B_{\p,\q}^{\bm{w}}(\rn)$ and $F_{\p,\q}^{\bm{w}}(\rn)$ in
order to get the main result.
