Sharp embedding results for spaces of smooth functions with power weights

Abstract

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.