Geodesic
Interpolation of Besov spaces in the nondiagonal case
Algebra i analiz, Tome 18 (2006) no. 4, pp. 1-9 
I. Asekritova; N. Kruglyak. Interpolation of Besov spaces in the nondiagonal case. Algebra i analiz, Tome 18 (2006) no. 4, pp. 1-9. http://geodesic.mathdoc.fr/item/AA_2006_18_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the nondiagonal case, interpolation spaces for a collection of Besov spaces are described. The results are consequences of the fact that, whenever the convex hull of points $(\bar s_0,\eta_0),\dots,(\bar s_n,\eta_n)\in \mathbb R^{m+1}$ includes a ball of $\mathbb R^{m+1}$, we have $$ (l^{\bar s_0}_{q_0}((X_0,X_1)_{\eta_0,p_0}),\dots,l^{\bar s_n}_{q_n}((X_0,X_1)_{\eta_n,p_n}))=l^{\bar s_{\bar{\theta}}}_q((X_0,X_1)_{\eta_{\bar{\theta}},q}), $$ where $\bar\theta=(\theta_0,\dots,\theta_n)$ and $(s_{\bar{\theta}},\eta_{\bar{\theta}})=\theta_0(\bar s_0, \eta_0)+\dots+\theta_n(\bar s_n,\eta_n)$.

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