We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of 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 d’une dimension donnée. Un théorème d’inclusion des traces correspondant avec une image précise est établi.
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
@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}, pages = {939--951}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {3}, year = {2010}, doi = {10.5802/aif.2543}, mrnumber = {2680820}, zbl = {1208.46029}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2543/} }
TY - JOUR AU - Cianchi, Andrea AU - Pick, Luboš TI - An optimal endpoint trace embedding JO - Annales de l'Institut Fourier PY - 2010 SP - 939 EP - 951 VL - 60 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2543/ DO - 10.5802/aif.2543 LA - en ID - AIF_2010__60_3_939_0 ER -
%0 Journal Article %A Cianchi, Andrea %A Pick, Luboš %T An optimal endpoint trace embedding %J Annales de l'Institut Fourier %D 2010 %P 939-951 %V 60 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2543/ %R 10.5802/aif.2543 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2543/
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