Interpolation of Besov spaces in the nondiagonal case

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

$(l^{\bar s_0}_{q_0}((X_0,X_1)_{\eta_0,p_0}),\dots, l^{\bar s_n}_{... ...ar{\theta},q}= l^{\bar s_{\bar{\theta}}}_q((X_0,X_1)_{\eta_{\bar{\theta}},q}),$

where $\bar\theta=(\theta_0,\dots,\theta_n)$ and $(s_{\bar{\theta}},\eta_{\bar{\theta}})=\theta_0(\bar s_0, \eta_0)+\dots +\theta_n(\bar s_n,\eta_n)$.