Sharp embedding results for spaces of smooth functions with power weights

Volume 208 / 2012

Martin Meyries, Mark Veraar Studia Mathematica 208 (2012), 257-293 MSC: 46E35, 46E40. DOI: 10.4064/sm208-3-5


We consider function spaces of Besov, Triebel–Lizorkin, Bessel-potential and Sobolev type on $\mathbb R^d$, 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.


  • Martin MeyriesDepartment of Mathematics
    Karlsruhe Institute of Technology
    76128 Karlsruhe, Germany
  • Mark VeraarDelft Institute of Applied Mathematics
    Delft University of Technology
    P.O. Box 5031
    2600 GA Delft, The Netherlands

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