A characterization of Sobolev spaces via local derivatives

David Swanson

David Swanson

Colloquium Mathematicae, Tome 120 (2010), p. 157-167 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $f \in W^{k, p} (Ω)$ 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.

Publié le : 2010-01-01

Zbl 1206.46036

EUDML-ID : urn:eudml:doc:284327

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     title = {A characterization of Sobolev spaces via local derivatives},
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     volume = {120},
     year = {2010},
     pages = {157-167},
     zbl = {1206.46036},
     language = {en},
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David Swanson. A characterization of Sobolev spaces via local derivatives. Colloquium Mathematicae, Tome 120 (2010) pp. 157-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-11/