A characterization of Sobolev spaces via local derivatives

David 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 -