An optimal endpoint trace embedding

Cianchi, Andrea; Pick, Luboš

Annales de l'Institut Fourier, Tome 60 (2010) no. 3, pp. 939-951.

Nous construisons un espace optimal du type Sobolev dont toutes les fonctions admettent une trace sur les sous-espaces de ${ℝ}^n$ d’une dimension donnée. Un théorème d’inclusion des traces correspondant avec une image précise est établi.

We find an optimal Sobolev-type space on ${ℝ}^n$ all of whose functions admit a trace on subspaces of ${ℝ}^n$ of given dimension. A corresponding trace embedding theorem with sharp range is established.

Classification : 46E35, 46E30
Keywords: Sobolev spaces, trace inequalities, Lorentz spaces, rearrangement invariant spaces
Mot clés : espaces de Sobolev, inégalités des traces, espaces de Lorentz, espaces invariants par réarrangementxs

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