Sharp embedding results for spaces of smooth functions with power weights

2011/12/22 by Meyries, Martin, Veraar, Mark · 1 citation
#46E35 #46E40 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1112.5388

Abstract

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on \R^d, equipped with power weights w(x) = |x|^γ, γ>-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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