2016/03/25 by Alexander Tyulenev, Tyulenev, A. I.
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1603.07841
openalex publication_date 2016/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The paper puts forward new Besov spaces of variable smoothness B^φ0p,q(G,\tk\) and \widetildeBlp,q,r(Ω,\tk\) on rough domains. A~domain~G is either a~bounded Lipschitz domain in~ℝn 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^φ0p,q(ℝn,\tk\) and \widetildeBlp,q,r(ℝn,\tk\) on domains G and~Ω, respectively. The extension operator Ext1:B^φ0p,q(G,\tk\) → B^φ0p,q(ℝn,\tk\) is linear, the operator Ext2:\widetildeBlp,q,r(Ω,\tk\) → \widetildeBlp,q,r(ℝn,\tk\) 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.