Sharp embedding results for spaces of smooth functions with power weights

By M. Meyries, Mark Veraar. 2011

71 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb125ac15942ca7ccde35a25c6290b76136aa5e4

Citations in the corpus

• Traces and embeddings of anisotropic function spaces (2012, unknown): “For the outer F -spaces, this is essentially a consequence of the Sobolev embeddings from [29] for weighted F -spaces with fixed integrability parameter p.”