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Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 89–104 (Mi tm3520)  

This article is cited in 5 scientific papers (total in 5 papers)

To the Sobolev embedding theorem for the limiting exponent

O. V. Besov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: We establish embeddings of the Sobolev space $W_p^s$ and the space $B_{pq}^s$ (with the limiting exponent) in certain spaces of locally integrable functions of zero smoothness. This refines the embedding of the Sobolev space in the Lorentz and Lorentz–Zygmund spaces. Similar problems are considered for the case of irregular domains and for the potential space.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00744
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation NSh-6431.2012.1
2.1.1/1662
This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00744), by the program "Modern Problems of Theoretical Mathematics" of the Russian Academy of Sciences, by a grant of the President of the Russian Federation (project no. NSh-6431.2012.1), and by the program "Development of the Scientific Potential of Higher Learning Institutions" of the Ministry of Education and Science of the Russian Federation (project no. 2.1.1/1662).


DOI: https://doi.org/10.1134/S0371968514010051

Full text: PDF file (249 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 81–96

Bibliographic databases:

Document Type: Article
UDC: 517.518.23+517.982.256
Received in November 2013

Citation: O. V. Besov, “To the Sobolev embedding theorem for the limiting exponent”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 89–104; Proc. Steklov Inst. Math., 284 (2014), 81–96

Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
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\yr 2014
\vol 284
\pages 89--104
\publ MAIK Nauka/Interperiodica
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Tyulenev, “Some new function spaces of variable smoothness”, Sb. Math., 206:6 (2015), 849–891  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. O. V. Besov, “Embedding of Sobolev Space in the Case of the Limit Exponent”, Math. Notes, 98:4 (2015), 550–560  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Tyulenev A.I., “Traces of Weighted Sobolev Spaces With Muckenhoupt Weight. the Case P=1”, Nonlinear Anal.-Theory Methods Appl., 128 (2015), 248–272  crossref  mathscinet  zmath  isi  scopus
    4. Besov O.V., “Embeddings of Sobolev Spaces in the Case of the Limit Exponent”, Dokl. Math., 91:3 (2015), 277–280  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    5. Besov O.V., “Embedding of Sobolev spaces with limit exponent revisited”, Dokl. Math., 94:3 (2016), 684–687  mathnet  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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