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This article is cited in 4 scientific papers (total in 4 papers)
Interpolation theorem for anisotropic net spaces
A. N. Bashirovaab, A. K. Kalidoldaya, E. D. Nursultanovc a L.N. Gumilyov Eurasian National University, 13 Kazhymukan Munaitpasov str., Nur-Sultan, Z01C0X0 Kazakhstan
b Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, A26G7T4 Kazakhstan
c M.V. Lomonosov Moscow State University, Kazakhstan Branch, 11 Kazhymukan Munaitpasov str., Nur-Sultan, Z01C0T6 Kazakhstan
Abstract:
The paper studies the interpolation properties of anisotropic net spaces $N_{\bar{p},\bar{q}}(M)$, where $\bar{p}=(p_1, p_2)$, $\bar{q}=(q_1, q_2)$. It is shown that the following equality holds with respect to the multidimensional interpolation method $$ (N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\bar{\theta},\bar{q}}=N_{\bar{p},\bar{q}}(M), \frac{1}{\bar{p}}=\frac{1-\bar{\theta}}{\bar{p}_0}+\frac{\bar{\theta}}{\bar{p}_1}. $$
Keywords:
net space, anisotropic space, real interpolation method.
Received: 27.08.2020 Revised: 14.12.2020 Accepted: 30.03.2021
Citation:
A. N. Bashirova, A. K. Kalidolday, E. D. Nursultanov, “Interpolation theorem for anisotropic net spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 8, 3–15; Russian Math. (Iz. VUZ), 65:8 (2021), 1–12
Linking options:
https://www.mathnet.ru/eng/ivm9698 https://www.mathnet.ru/eng/ivm/y2021/i8/p3
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