Geodesic
Sobolev-type functions on nonhomogeneous metric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 690-699 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider analogs of classical embedding theorems for function classes of Sobolev type on nonhomogeneous metric measure spaces.
Keywords: metric, measure, embedding theorems. 
@article{SEMR_2020_17_a131,
     author = {A. S. Romanov},
     title = {Sobolev-type functions on~nonhomogeneous metric spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {690--699},
     year = {2020},
     volume = {17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a131/}
}
TY  - JOUR
AU  - A. S. Romanov
TI  - Sobolev-type functions on nonhomogeneous metric spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 690
EP  - 699
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a131/
LA  - en
ID  - SEMR_2020_17_a131
ER  - 
%0 Journal Article
%A A. S. Romanov
%T Sobolev-type functions on nonhomogeneous metric spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 690-699
%V 17
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a131/
%G en
%F SEMR_2020_17_a131
A. S. Romanov. Sobolev-type functions on nonhomogeneous metric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 690-699. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a131/

[1] P. Hajlasz, “Sobolev spaces on an arbitrary metric space”, Potential Anal., 5:4 (1996), 403–415 | MR | Zbl

[2] P. Hajlasz, J. Kinnunen, “Hölder quasicontinuity of Sobolev functions”, Rev. Mat. Iberoam., 14:3 (1998), 601–622 | DOI | MR | Zbl

[3] P. Hajlasz, P. Koskela, Sobolev Met Poincare, Mem. Am. Math. Soc., 688, 2000 | MR | Zbl

[4] A.S. Romanov, “Traces of functions of generalized Sobolev classes”, Sib. Mat. Zh., 48:4 (2007), 848–866 | Zbl

[5] A.L. Vol'berg, S.V. Konyagin, “There is a homogeneous measure on any compact subset in $R^n$”, Sov. Math., Dokl., 30 (1984), 453–456 | MR | Zbl

[6] O. Kovacik, J. Rakosnik, “On spaces $L^{p(x)}$ and $W^{k,p(x)}$”, Czech. Math. J., 41:4 (1991), 592–618 | DOI | MR | Zbl

[7] A.S. Romanov, “Sobolev-type functions with variable integrability exponent on metric measure spaces”, Sib. Math. J., 55:1 (2014), 142–155 | DOI | MR | Zbl