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.
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.
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
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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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