Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces

• Autorzy: Rémi Arcangéli , Juan José Torrens
• Języki publikacji: EN

Abstrakty

EN

We collect and extend results on the limit of $σ^{1-k}(1-σ)^{k}|v|_{l+σ,p,Ω}^{p}$ as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ {0,1}, l ∈ ℕ, p ∈ [1,∞), and $|·|_{l+σ,p,Ω}$ is the intrinsic seminorm of order l+σ in the Sobolev space $W^{l+σ,p}(Ω)$. In general, the above limit is equal to $c[v]^{p}$, where c and [·] are, respectively, a~constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 46F12: Integral transforms in distribution spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 2
• Strony: 101-120

Daty

wydano

2013

Twórcy

autor

Rémi Arcangéli

• Retired Professor, Route de Barat, 31160 Arbas, France

autor

Juan José Torrens

• Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain

Identyfikatory

DOI

10.4064/sm214-2-1