  We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and
Sobolev type on $\R^d$, equipped with power weights $w(x) = |x|^\gamma$,
$\gamma>-d$. We prove two-weight Sobolev embeddings for these spaces. Moreover,
we precisely characterize for which parameters the embeddings hold. The proofs
are presented in such a way that they also hold for vector-valued functions.
