Geodesic
On the continuity of Sobolev-type functions on homogeneous metric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 460-483

Voir la notice de l'article provenant de la source Math-Net.Ru

On $s$-homogeneous metric spaces with measure for Sobolev-type functions with "smoothness" $\alpha \le 1$ we prove the property $s/\alpha$- absolute continuity, in the case when the characteristics that define "smoothness" belong to the corresponding Lorentz space.
Keywords: Lorentz space, Sobolev type functions, homogeneous metric spaces, absolute continuity. 
@article{SEMR_2022_19_2_a48,
     author = {A. S. Romanov},
     title = {On the continuity of {Sobolev-type} functions on homogeneous metric spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {460--483},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a48/}
}
TY  - JOUR
AU  - A. S. Romanov
TI  - On the continuity of Sobolev-type functions on homogeneous metric spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 460
EP  - 483
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a48/
LA  - ru
ID  - SEMR_2022_19_2_a48
ER  - 
%0 Journal Article
%A A. S. Romanov
%T On the continuity of Sobolev-type functions on homogeneous metric spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 460-483
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a48/
%G ru
%F SEMR_2022_19_2_a48
A. S. Romanov. On the continuity of Sobolev-type functions on homogeneous metric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 460-483. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a48/