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Eurasian Mathematical Journal, 2024, Volume 15, Number 2, Pages 33–41
DOI: https://doi.org/10.32523/2077-9879-2024-15-2-33-41
(Mi emj499)
 

Interpolation methods for anisotropic net spaces

A. N. Bashirovaa, A. K. Kalidoldayb, E. D. Nursultanovbc

a Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan St, 010008 Astana, Kazakhstan
b Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
c Department of Mathematics and Informatics, M.V.Lomonosov Moscow State University (Kazakhstan branch), 11 Kazhymukan St, 010010 Astana, Kazakhstan
References:
Abstract: In this paper, we study the interpolation properties of anisotropic net spaces $N_{\overline{p},\overline{q}}(M)$, where $\overline{p} = (p_1,\dots, p_n)$, $\overline{q} = (q_1,\dots, q_n)$. It is shown that, with respect to the multidimensional interpolation method, the following equality holds
$$ (N_{\overline{p}_0,{\overline{q}_0}}(M), N_{\overline{p}_1,{\overline{q}_1}}(M))_{\overline{\theta},\overline{q}}=N_{\overline{p},\overline{q}}(M),\qquad \frac1{\overline{p}}=\frac{1-\overline{\theta}}{\overline{p}_0}+\frac{\overline{\theta}}{\overline{p}_1}. $$
Keywords and phrases: net spaces, anisotropic spaces, real interpolation method.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP14870361
This research was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (project no. AP14870361).
Received: 03.07.2023
Document Type: Article
MSC: 46B70
Language: English
Citation: A. N. Bashirova, A. K. Kalidolday, E. D. Nursultanov, “Interpolation methods for anisotropic net spaces”, Eurasian Math. J., 15:2 (2024), 33–41
Citation in format AMSBIB
\Bibitem{ShaKalNur24}
\by A.~N.~Bashirova, A.~K.~Kalidolday, E.~D.~Nursultanov
\paper Interpolation methods for anisotropic net spaces
\jour Eurasian Math. J.
\yr 2024
\vol 15
\issue 2
\pages 33--41
\mathnet{http://mi.mathnet.ru/emj499}
\crossref{https://doi.org/10.32523/2077-9879-2024-15-2-33-41}
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