Trace theorem on the Heisenberg group
Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 491-514.

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

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.

Received:
Accepted:
DOI: 10.5802/aif.2437
Classification: 35Axx,  35Hxx,  35Sxx
Keywords: Trace and trace lifting, Heisenberg group, Hörmander condition, Hardy’s inequality
Bahouri, Hajer 1; Chemin, Jean-Yves 2; Xu, Chao-Jiang 3

1 Faculté de Sciences de Tunis Département de Mathématiques 1060 Tunis (Tunisie )
2 Université Paris 6 UMR 7598, Laboratoire J.-L. Lions 75230 Paris Cedex 05 (France)
3 Université de Rouen Laboratoire de Mathématiques, UMR-6085 Avenue de l’Université, BP 12 76801 Saint-Étienne du Rouvray (France)
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Bahouri, Hajer; Chemin, Jean-Yves; Xu, Chao-Jiang. Trace theorem on the Heisenberg group. Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 491-514. doi : 10.5802/aif.2437. https://aif.centre-mersenne.org/articles/10.5802/aif.2437/

[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

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