An optimal endpoint trace embedding
Annales de l'Institut Fourier, Volume 60 (2010) no. 3, p. 939-951

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.

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.

DOI : https://doi.org/10.5802/aif.2543
Classification:  46E35,  46E30
Keywords: Sobolev spaces, trace inequalities, Lorentz spaces, rearrangement invariant spaces
@article{AIF_2010__60_3_939_0,
     author = {Cianchi, Andrea and Pick, Lubo\v s},
     title = {An optimal endpoint trace embedding},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {3},
     year = {2010},
     pages = {939-951},
     doi = {10.5802/aif.2543},
     mrnumber = {2680820},
     zbl = {1208.46029},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_3_939_0}
}
Cianchi, Andrea; Pick, Luboš. An optimal endpoint trace embedding. Annales de l'Institut Fourier, Volume 60 (2010) no. 3, pp. 939-951. doi : 10.5802/aif.2543. http://www.numdam.org/item/AIF_2010__60_3_939_0/

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