Abstract
I would like to report on a joint work with Michel Ledoux; this work is still in progress and I shall only sketch here some general ideas and tentative results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Bakry, M. Emery, Inégalités de Sobolev pour un semi-groupe symétrique, C.R. Acad. Sci. Paris 301, sér. I, 8 (1985), 411–413.
I. Chavel, E. Feldman, Isoperimetric constants, the geometry of ends, and large time heat diffusion in riemannian manifolds, Proc. Lond. Math. Soc., 3, 62 (1991), 427–448.
I. Chavel, E. Feldman, Modified isoperimetric constants and large time heat diffusion in riemannian manifolds, preprint.
T. Coulhon, Dimension à l’infini d’un semi-groupe analytique, Bull. Sc. Math. 114, 3 (1990), 485–500.
T. Coulhon, Dimensions of continuous and discrete semigroups, in “Semigroup Theory and Evolution Equations,” Clément, Mitidieri, de Pagter, eds, Marcel Dekker, Lect. Notes in Pure and Appl. Math., 1991, pp. 93-99.
T. Coulhon, Noyau de la chaleur et discrétisation d’une variété riemannienne, preprint.
B. Davies, Heat Kernels and Spectral Theory, Cambridge Univ. Press (1989).
P. Gerl, Sobolev inequalities and random walks, in “Probability Measures on Groups VIII,” Lect. Notes Math. 1210, Springer-Verlag, 1986, pp. 84–96.
R. Greene, H. Wu, “Function theory on manifolds which possess a pole,” Lect. Notes Math. 699, Springer-Verlag, 1976.
M. Kanai, Analytic inequalities, and rough isometries between non-compact riemannian manifolds, in “Curvature and Topology of Riemannian Manifolds,” Lect. Notes Math. 1201, Springer-Verlag, 1986, pp. 122–137.
Li P., Yau S. On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153–201.
V. Maz’ja, Classes of Domains, Measures and Capacities in the Theory of Differentiate Functions, in “Analysis III,” Encyclopedia of Mathematical Sciences, Springer-Verlag, 1991.
L. Saloff-Coste, Analyse sur les groupes de Lie à croissance polynômiale, Arkiv Mat. 28 2 (1990), 315–331.
N. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 2 (1985), 240–260.
N. Varopoulos, Analysis on Nilpotent Groups, J. Funct. Anal. 66 3 (1986), 406–431.
N. Varopoulos, Analysis on Lie Groups, J. Funct. Anal. 76 2 (1988), 346–410.
N. Varopoulos, Small time gaussian estimates of heat diffusion kernels. Part I: the semigroup technique, Bull. Sc. Math. 113 (1989), 253–277.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Coulhon, T. (1992). Sobolev Inequalities on Graphs and on Manifolds. In: Picardello, M.A. (eds) Harmonic Analysis and Discrete Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2323-3_16
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2323-3_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2325-7
Online ISBN: 978-1-4899-2323-3
eBook Packages: Springer Book Archive