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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
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.
Received: 03.07.2023
Citation:
A. N. Bashirova, A. K. Kalidolday, E. D. Nursultanov, “Interpolation methods for anisotropic net spaces”, Eurasian Math. J., 15:2 (2024), 33–41
Linking options:
https://www.mathnet.ru/eng/emj499 https://www.mathnet.ru/eng/emj/v15/i2/p33
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Abstract page: | 48 | Full-text PDF : | 15 | References: | 11 |
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