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.
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.
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
@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}, zbl = {1208.46029}, mrnumber = {2680820}, language = {en}, url = {http://www.numdam.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 - http://www.numdam.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 http://www.numdam.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, Tome 60 (2010) no. 3, pp. 939-951. doi : 10.5802/aif.2543. http://www.numdam.org/articles/10.5802/aif.2543/
[1] Sobolev spaces, Academic Press, New York-London, 1975 (Pure and Applied Mathematics, Vol. 65) | MR | Zbl
[2] Interpolation of operators, Pure and Applied Mathematics, 129, Academic Press Inc., Boston, MA, 1988 | MR | Zbl
[3] A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations, Volume 5 (1980) no. 7, pp. 773-789 | DOI | MR | Zbl
[4] Sobolev spaces on domains, Teubner-Texte zur Mathematik, 137, B. G. Teubner, Stuttgart, 1998 | MR | Zbl
[5] Boundary trace inequalities and rearrangements, J. Anal. Math., Volume 105 (2008), pp. 241-265 | DOI | MR | Zbl
[6] Sobolev embeddings into BMO, VMO, and , Ark. Mat., Volume 36 (1998) no. 2, pp. 317-340 | DOI | MR | Zbl
[7] On the modulus of continuity of Sobolev functions (preprint)
[8] Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities, Sobolev Spaces in Mathematics. II (Int. Math. Ser. (N. Y.)), Volume 9, Springer, New York, 2009, pp. 103-121 | MR | Zbl
[9] Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms, J. Funct. Anal., Volume 170 (2000) no. 2, pp. 307-355 | DOI | MR | Zbl
[10] Imbedding theorems of Sobolev type in potential theory, Math. Scand., Volume 45 (1979) no. 1, pp. 77-102 | MR | Zbl
[11] Optimal Sobolev imbeddings, Forum Math., Volume 18 (2006) no. 4, pp. 535-570 | DOI | MR | Zbl
[12] Sobolev spaces, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1985 | MR
[13] Convolution operators and spaces, Duke Math. J., Volume 30 (1963), pp. 129-142 | DOI | MR | Zbl
[14] Integral transforms and tensor products on Orlicz spaces and spaces, J. Analyse Math., Volume 21 (1968), pp. 1-276 | DOI | MR | Zbl
[15] Espaces d’interpolation et théorème de Soboleff, Ann. Inst. Fourier (Grenoble), Volume 16 (1966) no. fasc. 1, pp. 279-317 | DOI | Numdam | MR | Zbl
[16] Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970 | MR | Zbl
[17] Editor’s note: the differentiability of functions in , Ann. of Math. (2), Volume 113 (1981) no. 2, pp. 383-385 | MR | Zbl
[18] Inequalities in rearrangement invariant function spaces, Nonlinear analysis, function spaces and applications, Vol. 5 (Prague, 1994), Prometheus, Prague, 1994, pp. 177-230 | MR | Zbl
[19] Weakly differentiable functions, Graduate Texts in Mathematics, 120, Springer-Verlag, New York, 1989 (Sobolev spaces and functions of bounded variation) | MR | Zbl
Cité par Sources :