Traces and extensions of generalized smoothness Morrey spaces on domains

We study traces on the boundary of generalized smoothness Morrey spaces on C k domains Ω . These spaces are equipped with three parameters s , p , q and a function parameter φ . Our results remain valid for the usual Besov–Morrey spaces N u , p , q s ( Ω ) , Triebel–Lizorkin–Morrey spaces E u , p , q s ( Ω ) , and Triebel–Lizorkin type spaces F p , q s , τ ( Ω ) , which are all included in our scales as special cases. Moreover, to complete our investigation, we also study traces of Besov-type spaces B p , q s , τ ( Ω ) , which are not covered by our approach and give some applications in terms of a priori estimates generalizing results from El Baraka (2005).