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Russian Mathematical Surveys, 2019, Volume 74, Issue 6, Pages 1075–1115
DOI: https://doi.org/10.1070/RM9873 (Mi rm9873) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line

D. V. Prokhorova, V. D. Stepanovab, E. P. Ushakovac

a Computing Centre of the Far Eastern Branch of Russian Academy of Sciences, Khabarovsk
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
English version PDF (758 kB) Citations (8) Russian version article
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DOI: https://doi.org/10.1070/RM9873
Abstract: A brief survey of results on the characterization of the spaces associated with given classes of function spaces is presented. It is shown that the situation differs in general for ideal and non-ideal spaces. In the second case the notion of associated space splits into two. In the main body of the text a complete description is given of the function spaces associated with weighted Sobolev spaces of the first order on the real line.
Bibliography: 54 titles.
Keywords: function spaces, associated spaces, duality principle, weighted Sobolev spaces, Oinarov–Otelbaev construction, Hardy–Steklov integral operators.
Funding agency Grant number
Russian Science Foundation 14-11-00443
19-11-00087
The work of the first author was supported by the Russian Science Foundation under grant no. 14-11-00443 and carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences. The work of the second and third authors (Sections 3-5) was supported by the Russian Science Foundation under grant no. 19-11-00087 and also carried out at the Steklov Institute.
Received: 28.12.2018
Revised: 30.09.2019
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: Primary 46E35; Secondary 46E30
Language: English
Original paper language: Russian
Citation: D. V. Prokhorov, V. D. Stepanov, E. P. Ushakova, “Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line”, Russian Math. Surveys, 74:6 (2019), 1075–1115
Citation in format AMSBIB
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\paper Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line
\jour Russian Math. Surveys
\yr 2019
\vol 74
\issue 6
\pages 1075--1115
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  • https://www.mathnet.ru/eng/rm/v74/i6/p119
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:74
    English version PDF:49
    References:57
    First page:29
     
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