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Trudy Mat. Inst. Steklova, 2021, Volume 312, Pages 251–258 (Mi tm4138)  

On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces

V. D. Stepanovab, G. E. Shambilovac

a Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia

Abstract: We characterize a two-dimensional bilinear inequality with rectangular Hardy operators in weighted norms of Lebesgue spaces.

Funding Agency Grant Number
Russian Science Foundation 19-11-00087
Russian Foundation for Basic Research 19-01-00223
Ministry of Science and Higher Education of the Russian Federation
The work of V. D. Stepanov presented in Theorems 4 and 5 was supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. The work of V. D. Stepanov presented in the other 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. The work of G. E. Shambilova (Theorem 6) was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00223.


DOI: https://doi.org/10.4213/tm4138

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English version:
Proceedings of the Steklov Institute of Mathematics, 2021, 312, 241–248

Bibliographic databases:

UDC: 517.51
Received: May 24, 2020
Revised: September 6, 2020
Accepted: September 16, 2020

Citation: V. D. Stepanov, G. E. Shambilova, “On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 251–258; Proc. Steklov Inst. Math., 312 (2021), 241–248

Citation in format AMSBIB
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\by V.~D.~Stepanov, G.~E.~Shambilova
\paper On Two-Dimensional Bilinear Inequalities with Rectangular Hardy Operators in Weighted Lebesgue Spaces
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 251--258
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4138}
\crossref{https://doi.org/10.4213/tm4138}
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\jour Proc. Steklov Inst. Math.
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\pages 241--248
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