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
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.
function spaces, associated spaces, duality principle, weighted Sobolev spaces, Oinarov–Otelbaev construction, Hardy–Steklov integral operators.
|Russian Science Foundation
|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.
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Russian Mathematical Surveys, 2019, 74:6, 1075–1115
MSC: Primary 46E35; Secondary 46E30
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
Citation in format AMSBIB
\by D.~V.~Prokhorov, V.~D.~Stepanov, E.~P.~Ushakova
\paper Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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