Advertisement

Trace theorem on the Heisenberg group on homogeneous hypersurfaces

  • Hajer Bahouri
  • Jean-Yves Chemin
  • Chao-Jiang Xu
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 69)

Abstract

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

Key words

Trace and trace lifting Heisenberg group Hörmander condition Hardy’s inequality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Bahouri, J.-Y. Chemin and C.-J. Xu, Trace theorem on the Heisenberg group, preprint du Laboratoire J.-L. Lions, Université de Paris VI, 2006.Google Scholar
  2. 2.
    H. Bahouri, J.-Y. Chemin and I. Gallagher, Precise Hardy inequality ond and on the Heisenberg groupd, Séminaire EDP de l’École Polytechnique, 2005.Google Scholar
  3. 3.
    H. Bahouri, J.-Y. Chemin and C.-J. Xu, Trace and trace lifting theorems in weighted Sobolev space, J. Inst. Math Jussieu 4(2005), 509–552.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    H. Bahouri and I. Gallagher, Paraproduit sur le groupe de Heisenberg et applications, Rev. Math. IberoAmericana 17(2001), 69–105.zbMATHMathSciNetGoogle Scholar
  5. 5.
    H. Bahouri, P. Gérard and C.-J. Xu, Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. Math. 82(2000), 93–118.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    S. Berhanu and I. Pesenson, The trace problem for vector field satisfying Hörmander’s condition, Math. Z. 231(1999), 103–122.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J.-M. Bony and J.-Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. Math. France 122(1994), 77–118.zbMATHMathSciNetGoogle Scholar
  8. 8.
    C. E. Cancelier, J.-Y. Chemin and C.-J. Xu, Calcul de Weyl-Hörmander et opérateurs sous-elliptiques, Ann. Inst. Fourier (Grenoble) 43(1993), 1157–1178.zbMATHMathSciNetGoogle Scholar
  9. 9.
    J.-Y. Chemin and C.-J. Xu, Inclusions de Sobolev en calcul de Weyl-Hörmander et champs de vecteurs sous-elliptiques, Ann. Sci. École Norm. Sup. 30(1997), 719–751.zbMATHMathSciNetGoogle Scholar
  10. 10.
    D. Danielli, N. Garofalo and D-M. Nhieu, Trace inequalities for Carnot-Carathédory spaces and applications, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27(1998), 195–252.zbMATHMathSciNetGoogle Scholar
  11. 11.
    I. Pesenson, The trace Problem and Hardy operator for non-isotropic function spaces on the Heisenberg group, Comm. Partial Differential Equations 19(1994), 655–676.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Hajer Bahouri
    • 1
  • Jean-Yves Chemin
    • 2
  • Chao-Jiang Xu
    • 3
  1. 1.Département de MathématiquesFaculté de Sciences de TunisTunisie
  2. 2.Laboratoire Jacques-Louis Lions and CNRS UMR 7598Université Pierre et Marie Curie-Paris 6France
  3. 3.Laboratoire de MathématiquesUniversité de RouenFrance

Personalised recommendations