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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 131–157
DOI: https://doi.org/10.4213/tm4129 (Mi tm4129) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications

V. I. Burenkovab, E. D. Nursultanovcd

a S. M. Nikol'skii Mathematical Institute, RUDN University, ul. Miklukho-Maklaya 6, Moscow, 117198 Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan Str. 11, Nur-Sultan, 010010, Kazakhstan
d Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, Pushkina Str. 125, Almaty, 050010, Kazakhstan
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DOI: https://doi.org/10.4213/tm4129
Abstract: We prove new interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. In particular, these theorems apply to Urysohn integral operators. We also obtain analogs of the Marcinkiewicz–Calderón and Stein–Weiss–Peetre interpolation theorems and establish a criterion of $(p,q)$ quasiweak boundedness of the Urysohn operator.
Funding agency Grant number
Russian Science Foundation 19-11-00087
Ministry of Education and Science of the Russian Federation 5-100
Ministry of Education and Science of the Republic of Kazakhstan AP08956157
AP08856479
The research of E. D. Nursultanov (Sections 1–4) was supported by the Ministry of Education and Science of the Republic of Kazakhstan, project nos. AP08856479 and AP08956157. The research of V. I. Burenkov presented in Sections 1–4 was supported by the Peoples' Friendship University of Russia and performed in the S. M. Nikol'skii Mathematical Institute within the Russian Academic Excellence Project. The research of V. I. Burenkov presented in Sections 5–7 was supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.
Received: May 22, 2020
Revised: August 3, 2020
Accepted: August 7, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 124–149
DOI: https://doi.org/10.1134/S0081543821010077
Bibliographic databases:
Document Type: Article
UDC: 517.518.28+517.988.5
Language: Russian
Citation: V. I. Burenkov, E. D. Nursultanov, “Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications”, 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, 131–157; Proc. Steklov Inst. Math., 312 (2021), 124–149
Citation in format AMSBIB
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\paper Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications
\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 131--157
\publ Steklov Math. Inst.
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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