  Shearlets on the cone provide Parseval frames for $L^2$. They also provide
near-optimal approximation for the class $\mathcal{E}$ of cartoon-like images.
Moreover, there are spaces associated to them other than $L^2$ and there exist
embeddings between these and classical spaces.
  We prove approximation properties of the cone-adapted shearlets in a more
general context, namely, when the target function belongs to a class or space
different to $\mathcal{E}$ and when the error is not necessarily measured in
the $L^2$-norm but in a much wider family of smoothness space of high
anisotropy.
