Traces of weighted Sobolev spaces. Old and new

Petru Mironescu (1) , Emmanuel Russ (2)

1 EDPA - Équations aux dérivées partielles, analyse
2 IF - Institut Fourier

We give short simple proofs of Uspenskii's results characterizing Besov spaces as trace spaces of weighted Sobolev spaces. We generalize Uspenskii's results and prove the optimality of these generalizations. We next show how classical results on the functional calculus in the Besov spaces can be obtained as straightforward consequences of the theory of weighted Sobolev spaces.

Mots clés: trace theory; weighted Sobolev spaces; Besov spaces; Littlewood-Paley decompositions; functional calculus

Domaines: Analyse fonctionnelle [math.FA]

Petru Mironescu, Emmanuel Russ. Traces of weighted Sobolev spaces. Old and new. Nonlinear Analysis: Theory, Methods and Applications, 2015, 119, pp.354--381. ⟨hal-01064025⟩