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Matematicheskie Zametki, 2019, Volume 105, Issue 1, Pages 108–122
DOI: https://doi.org/10.4213/mzm11936 (Mi mzm11936) 		 
This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (572 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11936
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.
Received: 17.01.2018
Revised: 30.03.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 1, Pages 91–103
DOI: https://doi.org/10.1134/S0001434619010103
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
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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    • This publication is cited in the following 4 articles:
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