Estimates of the Besov norms on the fractal boundary and applications. (Q1411749)

Let \(\Omega\) be a bounded domain in \({\mathbb R}^n\) such that \(\partial \Omega\) is a \(d\)-set with \(n-1 \leq d <n\). The author estimates the trace of functions belonging to some weighted Sobolev spaces in \(\Omega\) on \(\partial \Omega\) in terms of related Besov spaces \(B^\alpha_p (\partial \Omega)\) on \(\partial \Omega\). A corresponding extension operator from \(B^\alpha_p (\partial \Omega)\) into respective Sobolev spaces in \(\Omega\) is constructed. Applications to the boundedness of double layer potentials are given.