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

摘要

We provide non-smooth atomic decompositions for Besov spaces Bp,qs(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.