A characterization of Sobolev spaces via local derivatives

• Autorzy: David Swanson
• Języki publikacji: EN

Abstrakty

EN

Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function $f ∈ W^{k,p}(Ω)$ possesses an $L^{p}$ derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space $W^{k,p}(Ω)$. Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.

Kategorie tematyczne

• 26B35: Special properties of functions of several variables, H\"older conditions, etc.
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 119
• Numer: 1
• Strony: 157-167

Daty

wydano

2010

Twórcy

autor

David Swanson

• Department of Mathematics, University of Louisville, Louisville, KY 40292, U.S.A.

Identyfikatory

DOI

10.4064/cm119-1-11