We provide non-smooth atomic decompositions for Besov spaces \Bd(\rn), s>0, 0<p,q\leq \infty, defined via differences, with the help of a homogeneity property.

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.