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Eurasian Mathematical Journal, 2022, Volume 13, Number 4, Pages 61–69
DOI: https://doi.org/10.32523/2077-9879-2022-13-4-61-69 (Mi emj454) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Marcinkiewicz's interpolation theorem for linear operators on net spaces

A. K. Kalidoldaya, E. D. Nursultanovabc

a Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 5 Munaitpasov St, 010008 Astana, Kazakhstan
b Department of Mathematics and Informatics, M.V. Lomonosov Moscow State University (Kazakhstan branch), 11 Kazhimukan St, 010010 Astana, Kazakhstan
c Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2022-13-4-61-69
Abstract: In this paper, we study the interpolation properties of the net spaces $N_{p,q}(M)$. We prove some analogue of Marcinkiewicz's interpolation theorem. This theorem allows to obtain the strong boundedness of linear operators in the net spaces from the weak boundedness of these operators in the net spaces with local nets.
Keywords and phrases: interpolation spaces, net spaces, linear operators.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP14870758
This research was supported by the Ministry of Education and Science of the Republic of Kazakhstan (project no. AP14870758).
Received: 25.07.2021
Bibliographic databases:
Document Type: Article
MSC: 46B70
Language: English
Citation: A. K. Kalidolday, E. D. Nursultanov, “Marcinkiewicz's interpolation theorem for linear operators on net spaces”, Eurasian Math. J., 13:4 (2022), 61–69
Citation in format AMSBIB
\Bibitem{KalNur22}
\by A.~K.~Kalidolday, E.~D.~Nursultanov
\paper Marcinkiewicz's interpolation theorem for linear operators on net spaces
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 4
\pages 61--69
\mathnet{http://mi.mathnet.ru/emj454}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-4-61-69}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4537111}
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