Traces and extensions of generalized smoothness Morrey spaces on domains. (April 2019) - Moura, Susana; Neves, Júlio; Schneider, Cornelia
Abstract: 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).