Lebesgue points for Sobolev functions on metric spaces.

Kinnunen, Juha, and Latvala, Visa. "Lebesgue points for Sobolev functions on metric spaces.." Revista Matemática Iberoamericana 18.3 (2002): 685-700. <http://eudml.org/doc/39699>.

@article{Kinnunen2002,
abstract = {Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.},
author = {Kinnunen, Juha, Latvala, Visa},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de funciones lineales; Espacios de Sobolev; Espacios métricos; Sobolev spaces; maximal functions; capacity},
language = {eng},
number = {3},
pages = {685-700},
title = {Lebesgue points for Sobolev functions on metric spaces.},
url = {http://eudml.org/doc/39699},
volume = {18},
year = {2002},
}

TY - JOUR
AU - Kinnunen, Juha
AU - Latvala, Visa
TI - Lebesgue points for Sobolev functions on metric spaces.
JO - Revista Matemática Iberoamericana
PY - 2002
VL - 18
IS - 3
SP - 685
EP - 700
AB - Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.
LA - eng
KW - Espacios de funciones lineales; Espacios de Sobolev; Espacios métricos; Sobolev spaces; maximal functions; capacity
UR - http://eudml.org/doc/39699
ER -