# A characterization of Sobolev spaces via local derivatives

Colloquium Mathematicae (2010)

- Volume: 119, Issue: 1, page 157-167
- ISSN: 0010-1354

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topDavid Swanson. "A characterization of Sobolev spaces via local derivatives." Colloquium Mathematicae 119.1 (2010): 157-167. <http://eudml.org/doc/284327>.

@article{DavidSwanson2010,

abstract = {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.},

author = {David Swanson},

journal = {Colloquium Mathematicae},

keywords = {Sobolev space; Calderón-Zygmund class; distributional derivative; local derivative; Riesz potential},

language = {eng},

number = {1},

pages = {157-167},

title = {A characterization of Sobolev spaces via local derivatives},

url = {http://eudml.org/doc/284327},

volume = {119},

year = {2010},

}

TY - JOUR

AU - David Swanson

TI - A characterization of Sobolev spaces via local derivatives

JO - Colloquium Mathematicae

PY - 2010

VL - 119

IS - 1

SP - 157

EP - 167

AB - 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.

LA - eng

KW - Sobolev space; Calderón-Zygmund class; distributional derivative; local derivative; Riesz potential

UR - http://eudml.org/doc/284327

ER -

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