no. 2
Trace theorem on the Heisenberg group  [ Un théorème de trace sur le groupe d’Heisenberg ]
Annales de l'Institut Fourier, Tome 59 (2009) no. 2, pp. 491-514.

Dans ce travail, nous démontrons des théorèmes de trace et de relèvement pour les espaces de Sobolev sur le groupe de Heisenberg pour des hypersurfaces dont l’ensemble caractéristique est une sous-variété.

We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.

DOI : https://doi.org/10.5802/aif.2437
Classification : 35Axx,  35Hxx,  35Sxx
Mots clés : trace et relèvement, groupe d’Heisenberg, condition de Hörmander, inégalité de Hardy 
@article{AIF_2009__59_2_491_0,
     author = {Bahouri, Hajer and Chemin, Jean-Yves and Xu, Chao-Jiang},
     title = {Trace theorem on the Heisenberg group},
     journal = {Annales de l'Institut Fourier},
     pages = {491--514},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {2},
     year = {2009},
     doi = {10.5802/aif.2437},
     mrnumber = {2521425},
     zbl = {1176.46037},
     language = {en},
     url = {www.numdam.org/item/AIF_2009__59_2_491_0/}
}
Bahouri, Hajer; Chemin, Jean-Yves; Xu, Chao-Jiang. Trace theorem on the Heisenberg group. Annales de l'Institut Fourier, Tome 59 (2009) no. 2, pp. 491-514. doi : 10.5802/aif.2437. http://www.numdam.org/item/AIF_2009__59_2_491_0/

[1] Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle Refined Hardy inequalities, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Volume 5 (2006) no. 3, pp. 375-391 | EuDML 242839 | Numdam | MR 2274784 | Zbl 1121.43006

[2] Bahouri, Hajer; Chemin, Jean-Yves; Xu, Chao-Jiang Trace and trace lifting theorems in weighted Sobolev spaces, J. Inst. Math. Jussieu, Volume 4 (2005) no. 4, pp. 509-552 | Article | MR 2171730 | Zbl 1089.35016

[3] Bahouri, Hajer; Chemin, Jean-Yves; Xu, Chao-Jiang Trace theorem on the Heisenberg group on homogeneous hypersurfaces, Phase space analysis of partial differential equations (Progr. Nonlinear Differential Equations Appl.) Volume 69, Birkhäuser Boston, Boston, MA, 2006, pp. 1-15 | MR 2263202 | Zbl 1127.35322

[4] Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. Math., Volume 82 (2000), pp. 93-118 | Article | MR 1799659 | Zbl 0965.22010

[5] Bergh, Jöran; Löfström, Jörgen Interpolation spaces. An introduction, Springer-Verlag, Berlin, 1976 (Grundlehren der Mathematischen Wissenschaften, No. 223) | MR 482275 | Zbl 0344.46071

[6] Berhanu, S.; Pesenson, I. The trace problem for vector fields satisfying Hörmander’s condition, Math. Z., Volume 231 (1999) no. 1, pp. 103-122 | Article | MR 1696759 | Zbl 0924.46026

[7] Bony, Jean-Michel; Chemin, Jean-Yves Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. Math. France, Volume 122 (1994) no. 1, pp. 77-118 | EuDML 87683 | Numdam | MR 1259109 | Zbl 0798.35172

[8] Cancelier, C. E.; Chemin, J.-Y.; Xu, C. J. Calcul de Weyl et opérateurs sous-elliptiques, Ann. Inst. Fourier (Grenoble), Volume 43 (1993) no. 4, pp. 1157-1178 | Article | EuDML 75028 | Numdam | MR 1252940 | Zbl 0797.35008

[9] Chemin, Jean-Yves; Xu, Chao-Jian Inclusions de Sobolev en calcul de Weyl-Hörmander et champs de vecteurs sous-elliptiques, Ann. Sci. École Norm. Sup. (4), Volume 30 (1997) no. 6, pp. 719-751 | EuDML 82448 | Numdam | MR 1476294 | Zbl 0892.35161

[10] Danielli, Donatella; Garofalo, Nicola; Nhieu, Duy-Minh Trace inequalities for Carnot-Carathéodory spaces and applications, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 27 (1998) no. 2, p. 195-252 (1999) | Numdam | MR 1664688 | Zbl 0938.46036

[11] Huet, Denise Décomposition spectrale et opérateurs, Presses Universitaires de France, Paris, 1976 (Le Mathématicien, No. 16) | MR 473900 | Zbl 0334.47015

[12] Pesenson, I. The trace problem and Hardy operator for nonisotropic function spaces on the Heisenberg group, Comm. Partial Differential Equations, Volume 19 (1994) no. 3-4, pp. 655-676 | Article | MR 1265812 | Zbl 0813.31005