Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 823-834.

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An embedding theorem of weighted spaces of functions of positive smoothness defined on irregular domains of $n$-dimensional Euclidean space in weighted Lebesgue spaces is established. The theorem is formulated depending on geometric parameters of the domain of functions.
Keywords: embedding theorem, weighted spaces of functions of positive smoothness, irregular domain
Mots-clés : Lebesgue spaces.
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     author = {O. V. Besov},
     title = {Embeddings of {Weighted} {Spaces} of {Functions} of {Positive} {Smoothness} on {Irregular} {Domains} in {Lebesgue} {Space}},
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O. V. Besov. Embeddings of Weighted Spaces of Functions of Positive Smoothness on Irregular Domains in Lebesgue Space. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 823-834. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a2/

[1] O. V. Besov, “Vlozhenie prostranstva Soboleva i svoistva oblasti”, Matem. zametki, 96:3 (2014), 343–349 | DOI | MR | Zbl

[2] O. V. Besov, “Vlozhenie vesovogo prostranstva Soboleva i svoistva oblasti”, Izbrannye voprosy matematiki i mekhaniki, Tr. MIAN, 289, MAIK «Nauka/Interperiodika», M., 2015, 107–114 | DOI

[3] O. V. Besov, “Prostranstva funktsii polozhitelnoi gladkosti na neregulyarnykh oblastyakh”, Dokl. AN, 466:2 (2016), 133–136 | DOI | Zbl

[4] O. V. Besov, “Prostranstva funktsii polozhitelnoi gladkosti na neregulyarnykh oblastyakh”, Funktsionalnye prostranstva, teoriya priblizhenii, smezhnye razdely matematicheskogo analiza, Tr. MIAN, 293, MAIK «Nauka/Interperiodika», M., 2016, 62–72 | DOI | MR

[5] O. V. Besov, “Vlozheniya prostranstv funktsii polozhitelnoi gladkosti na neregulyarnykh oblastyakh v prostranstva Lebega”, Matem. zametki, 103:3 (2018), 336–345 | DOI | Zbl

[6] D. A. Labutin, “Vlozhenie prostranstv Soboleva na gëlderovykh oblastyakh”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 18, Tr. MIAN, 227, Nauka, MAIK «Nauka/Interperiodika», M., 1999, 170–179 | MR | Zbl

[7] T. Kilpeläinen, J. Malý, “Sobolev inequalities on sets with irregular boundaries”, Z. Anal. Anwend., 19:2 (2000), 369–380 | DOI | MR | Zbl

[8] O. V. Besov, “Teorema vlozheniya Soboleva dlya oblasti s neregulyarnoi granitsei”, Matem. sb., 192:3 (2001), 3–26 | DOI | MR | Zbl

[9] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR | Zbl

[10] O. V. Besov, “Prostranstva funktsii drobnoi gladkosti na neregulyarnoi oblasti”, Matem. zametki, 74:2 (2003), 163–183 | DOI | MR | Zbl

[11] O. V. Besov, “Prostranstva funktsii tipa Lizorkina–Tribelya na neregulyarnoi oblasti”, Teoriya funktsii i nelineinye uravneniya v chastnykh proizvodnykh, Tr. MIAN, 260, MAIK «Nauka/Interperiodika», M., 2008, 32–43 | MR | Zbl

[12] I. Genebashvili, A. Gogatishvili, V. Kokilashvili, M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Pitman Monogr. Surveys Pure Appl. Math., 92, Longman, Harlow, 1998 | MR | Zbl

[13] E. M. Stein, G. Weiss, “An extension of a theorem of Marcinkiewicz and some of its applikatios”, J. Math. Mech., 8:2 (1959), 263–284 | MR | Zbl

[14] O. V. Besov, “Vlozheniya vesovykh prostranstv funktsii polozhitelnoi gladkosti na neregulyarnykh oblastyakh v prostranstva Lebega”, Dokl. AN, 480:3 (2018), 265–269 | DOI | Zbl