Besov-type spaces of variable smoothness on rough domains. (November 2016)

• Record Type: Journal Article
• Authors: Tyulenev, A.I.
• Is Part Of: Nonlinear analysis. Volume 145(2016)
• Page Start: 176
• Page End: 198
• Publication Date: 2016-11
• Subjects: 46E35; Besov spaces of variables smoothness -- Rough domains -- Nonlinear approximation; 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.2016.08.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The paper puts forward new Besov spaces of variable smoothness B p, q φ 0 ( G, { t k } ) and B ˜ p, q, r l ( Ω, { t k } ) on rough domains. A domain G is either a bounded Lipschitz domain in R n or the epigraph of a Lipschitz function, a domain Ω is an ( ε, δ ) -domain. These spaces are shown to be the traces of the spaces B p, q φ 0 ( R n, { t k } ) and B ˜ p, q, r l ( R n, { t k } ) on domains G and Ω, respectively. The extension operator Ext 1 : B p, q φ 0 ( G, { t k } ) → B p, q φ 0 ( R n, { t k } ) is linear, the operator Ext 2 : B ˜ p, q, r l ( Ω, { t k } ) → B ˜ p, q, r l ( R n, { t k } ) is nonlinear. As a corollary, an exact description of the traces of 2-microlocal Besov-type spaces and weighted Besov-type spaces on rough domains is obtained.