Interpolation methods for anisotropic net spaces

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

Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 33-41

Résumé

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 $$ (N_{\overline{p}_0,{\overline{q}_0}}(M), N_{\overline{p}_1,{\overline{q}_1}}(M))_{\overline{\theta},\overline{q}}=N_{\overline{p},\overline{q}}(M),\qquad \frac1{\overline{p}}=\frac{1-\overline{\theta}}{\overline{p}_0}+\frac{\overline{\theta}}{\overline{p}_1}. $$