Interpolation theorem for anisotropic net spaces
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 $$ (N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\bar{\theta},\bar{q}}=N_{\bar{p},\bar{q}}(M),\;\;\; \frac{1}{\bar{p}}=\frac{1-\bar{\theta}}{\bar{p}_0}+\frac{\bar{\theta}}{\bar{p}_1}. $$
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.00609
- arXiv:
- arXiv:2009.00609
- Bibcode:
- 2020arXiv200900609B
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Functional Analysis;
- 42B35;
- 46B70
- E-Print:
- 15 pages