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Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains

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Abstract

We establish an embedding theorem for spaces of functions of positive smoothness defined on irregular domains of n-dimensional Euclidean space in spaces of the same type and obtain some closely related results.

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References

  1. O. V. Besov, “Embedding of Sobolev spaces and properties of the domain,” Mat. Zametki 96 (3), 343–349 (2014) [Math. Notes 96 (3), 326–331 (2014)].

    Article  MathSciNet  Google Scholar 

  2. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains,” Dokl. Akad. Nauk SSSR 466 (2), 133–136 (2016) [Dokl. Math. 93 (1), 13–15 (2016)].

    MathSciNet  MATH  Google Scholar 

  3. O. V. Besov, “Spaces of functions of positive smoothness on irregular domains,” in Trudy Mat. Inst. Steklova, Vol. 293: Function Spaces, Approximation Theory, and Related Problems of Mathematical Analysis (MAIK Nauka/Interperiodika, Moscow, 2016), pp. 62–72 [Proc. Steklov Inst. Math. 293, 56–6 (2016)].

    Google Scholar 

  4. D. A. Labutin, “Embedding of Sobolev spaces on Hölder domains,” in Trudy Mat. Inst. Steklova, Vol. 227: Investigations in the Theory of Differentiable Functions of Many Variables and Its Applications. Part 18 (Nauka, MAIK Nauka/Interperiodika, Moscow, 1999), pp. 170–179 [Proc. Steklov Inst. Math. 227, 163–172 (1999)].

    Google Scholar 

  5. T. Kilpeläinen and J. Malý, “Sobolev inequalities on sets with irregular boundaries,” Z. Anal. Anwendungen 19 (2), 369–380 (2000).

    Article  MathSciNet  Google Scholar 

  6. O. V. Besov, “Sobolev’s embedding theorem for a domain with irregular boundary,” Mat. Sb. 192 (3), 3–26 (2001) [Sb. Math. 192 (3), 323–346 (2001)].

    Article  MathSciNet  Google Scholar 

  7. O. V. Besov, “Embeddings of spaces of functions of positive smoothness on irregular domains in Lebesgue spaces,” Mat. Zametki 103 (3), 336–345 (2018) [Math. Notes 103 (3), 348–356 (2018)].

    Article  MathSciNet  Google Scholar 

  8. O. V. Besov, “Embeddings of weighted spaces of functions of positive smoothness on irregular domains in Lebesgue space,” Mat. Zametki 104 (6), 823–834 (2018) [Math. Notes 104 (6), 799–809 (2018)].

    Article  MathSciNet  Google Scholar 

  9. O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Embedding Theorems (Nauka, Moscow, 1996) [in Russian].

    MATH  Google Scholar 

  10. O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain,” Mat. Zametki 74 (2), 163–183 (2003) [Math. Notes 74 (2), 157–176 (2003)].

    Article  MathSciNet  Google Scholar 

  11. O. V. Besov, “Function spaces of Lizorkin–Triebel type on an irregular domain,” in Trudy Mat. Inst. Steklova, Vol. 260: Function Theory and Nonlinear Partial Differential Equations (MAIK Nauka/Interperiodika, Moscow, 2008), pp. 32–43 [Proc. Steklov Inst. Math. 260, 25–36 (2008)].

    Google Scholar 

  12. I. Genebashvili, A. Gogatishvili, V. Kokilashvili, and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneuos Type, in Pitman Monogr. Surveys Pure Appl. Math. (Longnan, Harlow, 1998), Vol. 92.

  13. O. V. Besov, “Spaces of functions of fractional smoothness on an irregular domain,” in Trudy Mat. Inst. Steklova, Vol. 269: Function Theory and Differential Equations, Collected papers. Dedicated to Academician SergeiMikhailovich Nikol’skii on the occasion of his 105th birthday (MAIK Nauka/Interperiodika, Moscow, 2010), pp. 31–51 [Proc. Steklov Inst. Math. 269, 25–45 (2010)].

    Google Scholar 

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Correspondence to O. V. Besov.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 4, pp. 491–505.

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Besov, O.V. Embeddings of Spaces of Functions of Positive Smoothness on Irregular Domains. Math Notes 106, 501–513 (2019). https://doi.org/10.1134/S0001434619090207

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  • DOI: https://doi.org/10.1134/S0001434619090207

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