Sharp embedding results for spaces of smooth functions with power weights

Martin Meyries ¹   ; Mark Veraar ²

¹ Department of Mathematics Karlsruhe Institute of Technology 76128 Karlsruhe, Germany
² Delft Institute of Applied Mathematics Delft University of Technology P.O. Box 5031 2600 GA Delft, The Netherlands

Studia Mathematica, Tome 208 (2012) no. 3, pp. 257-293

Résumé

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.

Détail

DOI : 10.4064/sm208-3-5

Keywords: consider function spaces besov triebel lizorkin bessel potential sobolev type mathbb equipped power weights gamma gamma d prove two weight sobolev embeddings these spaces moreover precisely characterize which parameters embeddings proofs presented vector valued functions