The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 55-66
Voir la notice de l'article provenant de la source Math-Net.Ru
In this paper we prove an analog of the Luzin theorem on correction for the Sobolev-type spaces on an arbitrary metric space, whose measure satisfies the doubling condition. The correcting function belongs to the Hölder class and approximates a given function in the metrics of the initial space. Dimensions of exceptional sets are evaluated in terms of Hausdorff volumes and capacities.
Keywords:
a metric space with a measure, Luzin approximation.
Mots-clés : Sobolev spaces
Mots-clés : Sobolev spaces
@article{IVM_2008_5_a6,
author = {V. G. Krotov and M. A. Prokhorovich},
title = {The {Luzin} approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {55--66},
publisher = {mathdoc},
number = {5},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/}
}
TY - JOUR AU - V. G. Krotov AU - M. A. Prokhorovich TI - The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2008 SP - 55 EP - 66 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/ LA - ru ID - IVM_2008_5_a6 ER -
%0 Journal Article %A V. G. Krotov %A M. A. Prokhorovich %T The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2008 %P 55-66 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/ %G ru %F IVM_2008_5_a6
V. G. Krotov; M. A. Prokhorovich. The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 55-66. http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/