On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on Lipschitz subgraph and Lipschitz domain

Abstract

Abstract. Having a given weight ρ(x) = τ (dist(x,∂ Ω)) defined on Lipschitz boundary domain Ω and an Orlicz function Ψ , we construct the subordinated weight ω(·,·) defined on ∂ Ω × ∂ Ω and extension operator Ext

Extension and trace for nonlocal operators

“…For information on extension theorems for local operators we refer the reader to the book of Adams and Fournier [1], and to Ka lamajska and Dhara [20] and Koskela, Soto and Wand [38].…”