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Mat. Zametki, 2015, Volume 98, Issue 4, Pages 498–510 (Mi mz10824)  

This article is cited in 2 scientific papers (total in 2 papers)

Embedding of Sobolev Space in the Case of the Limit Exponent

O. V. Besov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We establish the embeddings of the Sobolev space $W_p^s$ and the space $B_{pq}^s$ (in the case of the limit exponent) in the spaces of locally summable functions of zero smoothness. This refines the embeddings of the Sobolev space in the Lorentz space and in the Lorentz–Zygmund space. The relationship between the Lorentz spaces and the corresponding spaces of functions of zero smoothness is established. Similar embeddings of the spaces of potentials are determined.

Keywords: Sobolev space $W_p^s$, the space $B_{pq}^s$, locally summable function of zero smoothness, Lorentz space, Lorentz–Zygmund space, space of potentials.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00684
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Russian Foundation for Basic Research under grant 14-01-00684 and by the program "Present-Day Problems of Theoretical Mathematics" of the Russian Academy of Sciences.


DOI: https://doi.org/10.4213/mzm10824

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English version:
Mathematical Notes, 2015, 98:4, 550–560

Bibliographic databases:

Document Type: Article
UDC: 517.982.256
Received: 15.01.2015

Citation: O. V. Besov, “Embedding of Sobolev Space in the Case of the Limit Exponent”, Mat. Zametki, 98:4 (2015), 498–510; Math. Notes, 98:4 (2015), 550–560

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. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Math. Notes, 101:4 (2017), 608–618  mathnet  crossref  crossref  mathscinet  isi  elib
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