Sharp embedding results for spaces of smooth functions with power weights

Details Sharp embedding results for spaces of smooth functions with power weights Sharp embedding results for spaces of smooth functions with power weights

2011-12-22

arxiv.org/abs/1112.5388v3

Mathematics

Functional Analysis

accepted for publication in Studia Mathematica

Scientific paper

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.

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