  We provide non-smooth atomic decompositions for Besov spaces $\Bd(\rn)$,
$s>0$, $0<p,q\leq \infty$, defined via differences. The results are used to
compute the trace of Besov spaces on the boundary $\Gamma$ of bounded Lipschitz
domains $\Omega$ with smoothness $s$ restricted to $0<s<1$ and no further
restrictions on the parameters $p,q$. We conclude with some more applications
in terms of pointwise multipliers.
