Una nota sobre los espacios de Sobolev anisotropos vectoriales $L^p_\Gamma(E)\ast$

Let $E$ be a Fréchet space and let $\Gamma$ be a finite non-empty subset of $\mathbb{N}^n$ such that if $(\alpha_j)\in\Gamma$ then $(\beta_j)\in\Gamma$ whenever $0\leq\beta_j\leq\alpha_j$ for $j=1,\cdots,n$. In this note we prove that the vector-valued anisotropic Sobolev spaces $L^p_\Gamma(E):=\{f\in L^p(E):D^\alpha f\in L^p(E)$ for $\alpha\in\Gamma$\},$1\leq p < \infty$, have the approximation property if $E$ has this property.