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Eurasian Mathematical Journal, 2023, Volume 14, Number 4, Pages 47–62
DOI: https://doi.org/10.32523/2077-9879-2023-14-4-47-62 (Mi emj483) 		 
Two–dimensional bilinear inequality for rectangular Hardy operator and non–factorizable weights

R. Senguptaab, E. P. Ushakovac

a Laboratory of approximate methods and functional analysis, Computing Center of Far Eastern branch of Russian Academy of Sciences, 65 Kim Yu Chena St., Khabarovsk 680000, Russian Federation
b Laboratory of quantum algorithms for machine learning and optimisation, Center for Artificial Intelligence Technology, Skolkovo Institute of Science and Technology, the territory of the Innovation Center "Skolkovo", Bolshoy Boulevard, 30, p.1, Moscow 121205, Russian Federation
c Laboratory of optimal controlled systems, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya St., Moscow 117997, Russian Federation
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DOI: https://doi.org/10.32523/2077-9879-2023-14-4-47-62
Abstract: Necessary conditions and sufficient conditions are given for the validity of two–dimensional bilinear norm inequalities with rectangular Hardy operators in weighted Lebesgue spaces. The results are applicable for non–factorizable weights.
Keywords and phrases: rectangular Hardy operator, bilinear inequality, weighted Lebesgue norm.
Funding agency Grant number
Russian Science Foundation 22-21-00579
Ministry of Science and Higher Education of the Russian Federation
The research work of the first author presented in Section 3.1 was supported by the Russian Science Foundation (project no. 22-21-00579, https://rscf.ru/project/22-21-00579/). The work of both authors presented in rest part of the paper was carried out within the framework of the state task of the Ministry of Science and Higher Education of the Russian Federation to the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences and V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences.
Received: 02.06.2023
Document Type: Article
MSC: 26D10, 47G10
Language: English
Citation: R. Sengupta, E. P. Ushakova, “Two–dimensional bilinear inequality for rectangular Hardy operator and non–factorizable weights”, Eurasian Math. J., 14:4 (2023), 47–62
Citation in format AMSBIB
\Bibitem{SenUsh23}
\by R.~Sengupta, E.~P.~Ushakova
\paper Two–dimensional bilinear inequality for rectangular Hardy operator and non–factorizable weights
\jour Eurasian Math. J.
\yr 2023
\vol 14
\issue 4
\pages 47--62
\mathnet{http://mi.mathnet.ru/emj483}
\crossref{https://doi.org/10.32523/2077-9879-2023-14-4-47-62}
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