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Mat. Zametki, 2019, Volume 105, Issue 1, Pages 108–122 (Mi mz11936)  
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

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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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