Derivative Embeddings in Vector-Valued Morrey Spaces

We develop an intermediate-derivative theory for Banach-valued evolution classes with Morrey control in time. Let $E_0\hookrightarrow E$ be Banach spaces, $m\ge2$, $1<p<\infty$, and $0\leλ<1$. If $u\in\mathcal M^{p,λ}(E_0)$ and $u^{(m)}\in\mathcal M^{p,λ}(E)$, then every intermediate derivative sati