Geodesic
Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 53-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove embedding theorems for spaces of functions of positive smoothness defined on a Hölder domain of $n$-dimensional Euclidean space.
Keywords: embedding, spaces of functions of positive smoothness, Sobolev space.
Mots-clés : Hölder domain 
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     title = {Integral {Representations} and {Embeddings} of {Spaces} of {Functions} of {Positive} {Smoothness} on a {H\"older} {Domain}},
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O. V. Besov. Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 53-64. http://geodesic.mathdoc.fr/item/TM_2023_323_a2/

[1] O. V. Besov, “Sobolev's embedding theorem for a domain with irregular boundary”, Sb. Math., 192:3 (2001), 323–346 | DOI | DOI | MR | Zbl

[2] O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain”, Proc. Steklov Inst. Math., 269 (2010), 25–45 | DOI | MR | Zbl

[3] O. V. Besov, “Embedding of Sobolev spaces and properties of the domain”, Math. Notes, 96:3–4 (2014), 326–331 | DOI | DOI | MR | Zbl

[4] O. V. Besov, “Embeddings of spaces of functions of positive smoothness on a Hölder domain in Lebesgue spaces”, Math. Notes, 113:1–2 (2023), 18–26 | DOI | DOI | MR | Zbl

[5] Besov O.V., Ilin V.P., Nikolskii S.M., Integralnye predstavleniya funktsii i teoremy vlozheniya, 2-e izd., Nauka, M., 1996 | MR

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

[7] Kufner A., Maligranda L., Person L.-E., The Hardy inequality: About its history and some related results, Vydavatelský Servis, Pilsen, 2007 | MR | Zbl

[8] D. A. Labutin, “Embedding of Sobolev spaces on Hölder domains”, Proc. Steklov Inst. Math., 227 (1999), 163–172 | MR | Zbl

[9] V. G. Maz'ya and S. V. Poborchi, “Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains”, St. Petersburg Math. J., 18:4 (2007), 583–605 | DOI | MR | Zbl