Traces and extensions of generalized smoothness Morrey spaces on domains. (April 2019)

• Record Type: Journal Article
• Authors: Moura, Susana; Neves, Júlio; Schneider, Cornelia
• Is Part Of: Nonlinear analysis. Volume 181(2019)
• Page Start: 311
• Page End: 339
• Publication Date: 2019-04
• Subjects: 46E35; Generalized smoothness Morrey spaces -- Besov-type spaces -- Traces -- Extension operator -- Lift operator -- Quarkonial decomposition -- Smooth domains; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.003
• Languages: English
• ISSNs: 0362-546X

Abstract

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).