Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

We provide non-smooth atomic decompositions for Besov spaces Bs p,q (Rn), s > 0, 0 < p,q ∞, defined via differences. The results are used to compute the trace of Besov spaces on the boundary Γ of bounded Lipschitz domains Ω 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. © 2012 Elsevier Inc. All rights reserved