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This article is cited in 2 scientific papers (total in 2 papers)
Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis
V. D. Stepanovab, E. P. Ushakovaab a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Computer Centre of Far Eastern Branch RAS
Abstract:
Estimates of the norms of spaces associated to weighted first-order Sobolev spaces with various weight functions and summation parameters are established. As the main technical tool, boundedness criteria for the Hardy–Steklov integral operator with variable limits of integration in Lebesgue spaces on the real axis are used.
Keywords:
Sobolev space, Hardy–Steklov operator, duality principle.
Funding Agency |
Grant Number |
Russian Science Foundation  |
14-11-00443 16-41-02004 |
The research of the authors presented in Secs. 1, 2, and 4
was carried out at Steklov Mathematical Institute, Russian Academy of Sciences
and supported by the Russian Science Foundation under grant 14-11-00443.
The research presented in Sec. 3
was carried out at RUDN University
and supported by the Russian Science Foundation under grant 16-41-02004. |
Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/mzm11936
Full text:
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English version:
Mathematical Notes, 2019, 105:1, 91–103
Bibliographic databases:
UDC:
517.98 Received: 17.01.2018 Revised: 30.03.2018
Citation:
V. D. Stepanov, E. P. Ushakova, “Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis”, Mat. Zametki, 105:1 (2019), 108–122; Math. Notes, 105:1 (2019), 91–103
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz11936https://doi.org/10.4213/mzm11936 http://mi.mathnet.ru/eng/mz/v105/i1/p108
Citing articles on Google Scholar:
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This publication is cited in the following articles:
-
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
-
A. A. Vasil'eva, “Kolmogorov Widths of Weighted Sobolev Classes on an Interval with Conditions on the Zeroth and First Derivatives”, Math. Notes, 107:3 (2020), 522–524
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