- Tytuł:
- Linear extension operators for restrictions of function spaces to irregular open sets
- Autorzy:
- Rychkov, V. S.
- Powiązania:
- https://bibliotekanauki.pl/articles/1206076.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Sobolev spaces
Besov-Triebel-Lizorkin spaces
restrictions
extension operators
irregular domains
Hausdorff content
local polynomial approximation
complemented subspaces - Opis:
- Let an open set $Ω ⊂ ℝ^n$ satisfy for some 0≤d≤n and ε > 0 the condition: the $d$-Hausdorff content $H_d(Ω∩B) ≥ ε|B|^{d/n}$ for any ball B centered in Ω of volume |B|≤1. Let $H_p^s$ denote the Bessel potential space on $ℝ^n$ 1 < p < ∞,s > 0, and let $H_p^s[Ω]$ be the linear space of restrictions of elements of $H_p^s$ to Ω endowed with the quotient space norm. We find sufficient conditions for the existence of a linear extension operator for $H_p^s[Ω]$, i.e., a bounded linear operator $H_p^s[Ω]→H_p^s$ such that $ext⨍|_Ω}=⨍$ for all ⨍. The main result is that such an operator exists if (i) d > n-1 and s > (n-d)/min(p,2), or (ii) d≤n-1 and s-[s] > (n-d)/min(p,2). It is an open problem whether these assumptions are sharp.
- Źródło:
-
Studia Mathematica; 2000, 140, 2; 141-162
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł