Trace theorem on the Heisenberg group

Hajer Bahouri[1]; Jean-Yves Chemin[2]; Chao-Jiang Xu[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)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 2, page 491-514
  • ISSN: 0373-0956

Abstract

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

How to cite

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Bahouri, Hajer, Chemin, Jean-Yves, and Xu, Chao-Jiang. "Trace theorem on the Heisenberg group." Annales de l’institut Fourier 59.2 (2009): 491-514. <http://eudml.org/doc/10401>.

@article{Bahouri2009,
abstract = {We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.},
affiliation = {Faculté de Sciences de Tunis Département de Mathématiques 1060 Tunis (Tunisie ); Université Paris 6 UMR 7598, Laboratoire J.-L. Lions 75230 Paris Cedex 05 (France); Université de Rouen Laboratoire de Mathématiques, UMR-6085 Avenue de l’Université, BP 12 76801 Saint-Étienne du Rouvray (France)},
author = {Bahouri, Hajer, Chemin, Jean-Yves, Xu, Chao-Jiang},
journal = {Annales de l’institut Fourier},
keywords = {Trace and trace lifting; Heisenberg group; Hörmander condition; Hardy’s inequality; Sobolev spaces; trace and trace lifting; Hardy's inequality; characteristic hypersurfaces},
language = {eng},
number = {2},
pages = {491-514},
publisher = {Association des Annales de l’institut Fourier},
title = {Trace theorem on the Heisenberg group},
url = {http://eudml.org/doc/10401},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Bahouri, Hajer
AU - Chemin, Jean-Yves
AU - Xu, Chao-Jiang
TI - Trace theorem on the Heisenberg group
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 2
SP - 491
EP - 514
AB - We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.
LA - eng
KW - Trace and trace lifting; Heisenberg group; Hörmander condition; Hardy’s inequality; Sobolev spaces; trace and trace lifting; Hardy's inequality; characteristic hypersurfaces
UR - http://eudml.org/doc/10401
ER -

References

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  1. Hajer Bahouri, Jean-Yves Chemin, Isabelle Gallagher, Refined Hardy inequalities, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 5 (2006), 375-391 Zbl1121.43006MR2274784
  2. Hajer Bahouri, Jean-Yves Chemin, Chao-Jiang Xu, Trace and trace lifting theorems in weighted Sobolev spaces, J. Inst. Math. Jussieu 4 (2005), 509-552 Zbl1089.35016MR2171730
  3. Hajer Bahouri, Jean-Yves Chemin, Chao-Jiang Xu, Trace theorem on the Heisenberg group on homogeneous hypersurfaces, Phase space analysis of partial differential equations 69 (2006), 1-15, Birkhäuser Boston, Boston, MA Zbl1127.35322MR2263202
  4. Hajer Bahouri, Patrick Gérard, Chao-Jiang Xu, Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. Math. 82 (2000), 93-118 Zbl0965.22010MR1799659
  5. Jöran Bergh, Jörgen Löfström, Interpolation spaces. An introduction, (1976), Springer-Verlag, Berlin Zbl0344.46071MR482275
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  7. Jean-Michel Bony, Jean-Yves Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. Math. France 122 (1994), 77-118 Zbl0798.35172MR1259109
  8. C. E. Cancelier, J.-Y. Chemin, C. J. Xu, Calcul de Weyl et opérateurs sous-elliptiques, Ann. Inst. Fourier (Grenoble) 43 (1993), 1157-1178 Zbl0797.35008MR1252940
  9. Jean-Yves Chemin, Chao-Jian Xu, Inclusions de Sobolev en calcul de Weyl-Hörmander et champs de vecteurs sous-elliptiques, Ann. Sci. École Norm. Sup. (4) 30 (1997), 719-751 Zbl0892.35161MR1476294
  10. Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Trace inequalities for Carnot-Carathéodory spaces and applications, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 195-252 (1999) Zbl0938.46036MR1664688
  11. Denise Huet, Décomposition spectrale et opérateurs, (1976), Presses Universitaires de France, Paris Zbl0334.47015MR473900
  12. I. Pesenson, The trace problem and Hardy operator for nonisotropic function spaces on the Heisenberg group, Comm. Partial Differential Equations 19 (1994), 655-676 Zbl0813.31005MR1265812

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