An optimal endpoint trace embedding
[Une injection de trace limite optimale]
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 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 n all of whose functions admit a trace on subspaces of n of given dimension. A corresponding trace embedding theorem with sharp range is established.

DOI : 10.5802/aif.2543
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
Cianchi, Andrea 1 ; Pick, Luboš 2

1 Università di Firenze Dipartimento di Matematica e Applicazioni per l’Architettura Piazza Ghiberti 27 50122 Firenze (Italy)
2 Charles University Faculty of Mathematics and Physics Department of Mathematical Analysis Sokolovská 83 186 75 Praha 8 (Czech Republic)
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Cianchi, Andrea; Pick, Luboš. An optimal endpoint trace embedding. Annales de l'Institut Fourier, Tome 60 (2010) no. 3, pp. 939-951. doi : 10.5802/aif.2543. http://www.numdam.org/articles/10.5802/aif.2543/

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