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Mat. Zametki, 2017, Volume 101, Issue 4, Pages 503–515 (Mi mz11369)  

This article is cited in 1 scientific paper (total in 1 paper)

Another Note on the Embedding of the Sobolev Space for the Limiting Exponent

O. V. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The embedding of the Sobolev spaces $W_p^s(\mathbb{R}^n)$ in a Lizorkin-type space of locally summable functions of zero smoothness is established. This result is extended to the case of the embedding of Sobolev spaces on nonregular domains of $n$-dimensional Euclidean space. The formulation of the theorem depends on the geometric parameters of the domain of the functions.

Keywords: Sobolev space, Lizorkin space, embedding theorem, zero smoothness.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443
This work was supported by the Russian Science Foundation under grant 14-11-00443.


DOI: https://doi.org/10.4213/mzm11369

Full text: PDF file (481 kB)
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English version:
Mathematical Notes, 2017, 101:4, 608–618

Bibliographic databases:

UDC: 517.518.23
Received: 07.09.2016
Revised: 06.10.2016

Citation: O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Mat. Zametki, 101:4 (2017), 503–515; Math. Notes, 101:4 (2017), 608–618

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. S. Neves, B. Opic, “Optimal local embeddings of Besov spaces involving only slowly varying smoothness”, J. Approx. Theory, 254 (2020), UNSP 105393  crossref  mathscinet  isi
  • Математические заметки Mathematical Notes
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