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arXiv · 2009.00609

Interpolation theorem for anisotropic net spaces

A. N. Bashirova·A. H. Kalidolday·E. D. Nursultanov
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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 $$ (N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\bar{\theta},\bar{q}}=N_{\bar{p},\bar{q}}(M),\;\;\; \frac{1}{\bar{p}}=\frac{1-\bar{\theta}}{\bar{p}_0}+\frac{\bar{\theta}}{\bar{p}_1}. $$

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A. N. Bashirova, A. H. Kalidolday, E. D. Nursultanov. 2020-09-01. Interpolation theorem for anisotropic net spaces. https://arxiv.org/abs/2009.00609

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