Interpolation theorem for anisotropic net spaces

A. N. Bashirova ; A. K. Kalidolday ; E. D. Nursultanov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 3-15.

Résumé

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 $$ (N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\bar{\theta},\bar{q}}=N_{\bar{p},\bar{q}}(M), \frac{1}{\bar{p}}=\frac{1-\bar{\theta}}{\bar{p}_0}+\frac{\bar{\theta}}{\bar{p}_1}. $$

Détail

Keywords: net space, real interpolation method.
Mots-clés : anisotropic space

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