  We study nuclear embeddings for function spaces of generalised smoothness
defined on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^d$. This covers,
in particular, the well-known situation for spaces of Besov and
Triebel-Lizorkin spaces defined on bounded domains as well as some first
results for function spaces of logarithmic smoothness. In addition, we provide
some new, more general approach to compact embeddings for such function spaces,
which also unifies earlier results in different settings, including also the
study of their entropy numbers. Again we rely on suitable wavelet decomposition
techniques and the famous Tong result (1969) about nuclear diagonal operators
acting in $\ell_r$ spaces, which we could recently extend to the vector-valued
setting needed here.
