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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
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.
Received: 28.12.2018 Revised: 30.09.2019
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”, Uspekhi Mat. Nauk, 74:6(450) (2019), 119–158; Russian Math. Surveys, 74:6 (2019), 1075–1115
Linking options:
https://www.mathnet.ru/eng/rm9873https://doi.org/10.1070/RM9873 https://www.mathnet.ru/eng/rm/v74/i6/p119
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Abstract page: | 668 | Russian version PDF: | 74 | English version PDF: | 47 | References: | 56 | First page: | 29 |
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