Markus Biegert

On traces of Sobolev functions on the boundary of extension domains

Assume that Ω ⊂ ℝ N is a bounded W 1,p -extension domain and that μ is an upper d-Ahlfors measure on ∂Ω with p ∈ (1, N) and d ∈ (N-p, N). Then there exist continuous trace operators from W 1,p (Ω) into L q (∂Ω, dμ) and into B p β (dμ) for every q ∈ [1, dp/(N - p)] and every β ∈ (0,1 - (N - d)/p].