Inégalités de Sobolev-Orlicz non-uniformes

Gilles Carron

Colloquium Mathematicae (1998)

  • Volume: 77, Issue: 2, page 163-178
  • ISSN: 0010-1354

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Carron, Gilles. "Inégalités de Sobolev-Orlicz non-uniformes." Colloquium Mathematicae 77.2 (1998): 163-178. <http://eudml.org/doc/210581>.

@article{Carron1998,
author = {Carron, Gilles},
journal = {Colloquium Mathematicae},
keywords = {heat kernel; Sobolev inequalities; Orlicz spaces; complete Riemannian manifold; Orlicz function; Luxemburg norm; Sobolev-Orlicz inequality},
language = {eng},
number = {2},
pages = {163-178},
title = {Inégalités de Sobolev-Orlicz non-uniformes},
url = {http://eudml.org/doc/210581},
volume = {77},
year = {1998},
}

TY - JOUR
AU - Carron, Gilles
TI - Inégalités de Sobolev-Orlicz non-uniformes
JO - Colloquium Mathematicae
PY - 1998
VL - 77
IS - 2
SP - 163
EP - 178
LA - eng
KW - heat kernel; Sobolev inequalities; Orlicz spaces; complete Riemannian manifold; Orlicz function; Luxemburg norm; Sobolev-Orlicz inequality
UR - http://eudml.org/doc/210581
ER -

References

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  1. [A] A. Ancona, Théorie du potentiel sur des graphes et des variétés, Lecture Notes in Math. 1427, Springer, 1990. 
  2. [C1] G. Carron, Inégalités isopérimétriques de Faber-Krahn et conséquences, dans : Actes de la Table Ronde de Géométrie Différentielle en l'Honneur de M. Berger (Luminy, 1992), Sémin. Congr. 1, Soc. Math. France, 1996, 205-232. 
  3. [C2] G. Carron, Inégalités de Faber-Krahn et inclusion de Sobolev-Orlicz, Potential Anal. 7 (1997), 555-575. 
  4. [C3] G. Carron, Une suite exacte en L 2 -cohomologie, Duke Math. J., à paraître. 
  5. [C4] G. Carron, L 2 -cohomologie et inégalités de Sobolev, prépublication n°306 de l’Institut J. Fourier, 1994. 
  6. [C5] G. Carron, Inégalité de Hardy sur les variétés riemanniennes, J. Math. Pures Appl. 76 (1997), 883-891. 
  7. [C-G-T] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53. Zbl0493.53035
  8. [C-S.C] T. Coulhon et L. Saloff-Coste, Variétés riemanniennes isométriques à l'in- fini, Rev. Mat. Iberoamericana 11 (1995), 687-726. 
  9. [D] E. B. Davies, Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc. 55 (1997), 105-125. Zbl0879.35064
  10. [G1] A. A. Grigor'yan, Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana 10 (1994), 395-452. 
  11. [G2] A. A. Grigor'yan, On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds, Math. USSR-Sb. 56 (1987), 349-357. 
  12. [L-Y] P. Li and S. T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201. Zbl0611.58045
  13. [L] J. Lott, L 2 -cohomology of geometrically infinite hyperbolic 3-manifolds, Geom. Funct. Anal. 7 (1997), 81-119. Zbl0873.57014
  14. [Mu] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983. Zbl0557.46020
  15. [S] E. M. Stein, Topics in Harmonic Analysis Related to Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, 1970. Zbl0193.10502
  16. [V] N. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260. Zbl0608.47047

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