A note on poincaré, sobolev, and harnack inequalities

International Mathematics Research Notices

Volumn 1992, Issue 2, 1992, Pages 27-38

  Saloff Coste, L ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84963021360     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/S1073792892000047     Document Type: Article

References (26)

1. D. Bakry and M. Emery, “Diffusions hypercontractives” in Séminaire de Probabilités XIX, 1983/84, Lecture Notes in Math. 1123, Springer, Berlin, 1985, 177-207.
2. P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. 15 (1982), 213-230.
3. E. Carlen, S. Kusuoka, and D. Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré Non Linéaire 23 (1987), 245-287.
4. J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and geometry of complete Riemannian manifolds, J. Differential Geom. 17(1982), 15-53.
5. Th. Coulhon and L. Saloff-Coste, Isopérimetrie pour les groupes et les variétés, preprint, 1991.
6. C. Fefferman and D. H. Phong, “Subelliptic eigenvalue problems” in Proceedings of the Conference in Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth Math. Ser., Wadsworth, Belmont, California, 1981, 590-606.
7. Y. Guivarc’h, Mouvement brownien sur les revêtements d’une variété compacte, C.R. Acad. Sci. Paris Sér. I. Math. 292 (1981), 851-853.
8. D. Jerison, The Poincaré inequality for vector fields satisfying Hörmander condition, Duke Math. J. 53 (1986), 503-523.
9. D. Jerison and A. Sanchez-Calle, “Subelliptic second order differential operators” in Complex Analysis III, Proceedings, Univ. of Md., Lecture Notes in Math. 1277, Springer, Berlin, 1986, 47-77.
10. A. Koranyi and J. C. Taylor, Minimal solutions of the heat equation and uniqueness of the positive Cauchy problem on homogeneous spaces, Proc. Amer. Math. Soc. 94 (1985), 273-279.
11. S. Kusuoka and D. Stroock, Applications of Malliavin calculus, part 3, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), 391-442.
12. P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201.
13. T. Lyons and D. Sullivan, Function theory, random paths and covering spaces, J. Differential Geom. 19(1984), 299-323.
14. R. Melrose, “Propagation for the wave group of a positive subelliptic second-order differential operator” in Hyperbolic Equations and Related Topics, Katata/Kyoto, 1984, Academic, Boston, 1986, 181-192.
15. J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134.
16. J. Moser, On pointwise estimate for parabolic differential equations, Comm Pure Appl. Math. 24 (1971), 727-740.
17. D. Robinson, Elliptic Operators and Lie Groups, Oxford Univ. Press, Oxford, 1991.
18. L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynomiale, Ark. Mat. 28 (1990), 315-331.
19. L. Saloff-Coste, Opérateurs uniformément elliptiques sur les variétés riemanniennes, C.R. Acad. Sci. Paris Sér. I. Math. 312 (1991), 25-30.
20. L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, to appear in J. Differential Geom. [21] L. Saloff-Coste and D. Stroock, Opérateurs uniformément sous-elliptiques sur des groupes de Lie, J. Funct. Anal. 98 (1991), 97-121.
21. N. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260.
22. N. Varopoulos, Analysis on Lie groups, J. Funct. Anal. 76 (1988), 346-410.
23. N. Varopoulos, Fonctions harmoniques sur les groupes de Lie, C.R. Acad. Sci. Paris Sér. I Math. 304 (1987), 519-521.
24. N. Varopoulos, “Random walks and Brownian motion on manifolds” in Analisi Armonica, Spazi Sim- metrici e Teoria della Probabilità, Cortona, 1984, Sympos. Math. 29, Academic, London, 1987, 97-109.
25. N. Varopoulos, Distances associées aux opérateurs sous-elliptiques du second ordre, C.R. Acad. Sci. Paris Sér. I Math. 309 (1989), 663-667.
26. S.-T. Y au, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228.