Interpolation of Besov spaces in the nondiagonal case

Abstract:

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 \begin{equation*} (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}))_{\bar {\theta },q}= l^{\bar s_{\bar {\theta }}}_q((X_0,X_1)_{\eta _{\bar {\theta }},q}), \end{equation*} where $\bar \theta =(\theta _0,\dots ,\theta _n)$ and $(s_{\bar {\theta }},\eta _{\bar {\theta }})=\theta _0(\bar s_0, \eta _0)+\dots +\theta _n(\bar s_n,\eta _n)$.