Classes of Sobolev type on quasimetric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1447-1455.

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On quasimetric measure spaces, classes of functions of Sobolev type are defined. In the model cases, analogues of the classical imbedding theorems are proved.
Mots-clés : quasimetric
Keywords: Sobolev space, embedding theorem.
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A. S. Romanov. Classes of Sobolev type on quasimetric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1447-1455. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a124/

[1] A.V. Arutyunov, A.V. Greshnov, “Theory of $(q_1,q_2)$-quasimetric spaces and coincidence points”, Doklady Mathematics, 94:1 (2016), 434–437 | DOI | MR | Zbl

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

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

[4] P. Hajlasz, P. Koskela, “Sobolev met Poincare”, Memoirs AMS, 145, no. 688, 2000 | DOI | MR

[5] A.S. Romanov, “Embedding theorems for generalized Sobolev spaces”, Siberian Math. Journal, 40:4 (1999), 787–792 | DOI | MR

[6] A.S. Romanov, “Traces of functions of generalized Sobolev classes”, Siberian Math. Journal, 48:4 (2007), 678–693 | DOI | MR | Zbl

[7] A.S. Romanov, “Embedding Theorems for a Certain Function Class of Sobolev Type on Metric Spaces”, Siberian Math. Journal, 45:2 (2004), 376–387 | DOI | MR | Zbl

[8] A.S. Romanov, “On Embeddings for Classes of Functions with Generalized Smoothness on Metric Spaces”, Siberian Math. Journal, 45:4 (2004), 722–729 | DOI | MR | Zbl