Optimal heat kernel bounds under logarithmic Sobolev inequalities
ESAIM: Probability and Statistics, Tome 1 (1997), pp. 391-407 
@article{PS_1997__1__391_0,
     author = {Bakry, D. and Concordet, D. and Ledoux, M.},
     title = {Optimal heat kernel bounds under logarithmic {Sobolev} inequalities},
     journal = {ESAIM: Probability and Statistics},
     pages = {391--407},
     year = {1997},
     publisher = {EDP Sciences},
     volume = {1},
     mrnumber = {1486642},
     zbl = {0898.58052},
     language = {en},
     url = {https://www.numdam.org/item/PS_1997__1__391_0/}
}
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%A Concordet, D.
%A Ledoux, M.
%T Optimal heat kernel bounds under logarithmic Sobolev inequalities
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Bakry, D.; Concordet, D.; Ledoux, M. Optimal heat kernel bounds under logarithmic Sobolev inequalities. ESAIM: Probability and Statistics, Tome 1 (1997), pp. 391-407. https://www.numdam.org/item/PS_1997__1__391_0/

Aubin, Th. ( 1982), Nonlinear analysis on manifolds. Monge-Ampère equations, Springer. | Zbl | MR

Bakry, D. ( 1994), L'hypercontractivité et son utilisation en théorie des semigroupes, École d'Été de Probabilités de St-Flour, Lecture Notes in Math. 1581 1-114, Springer. | Zbl | MR

Bakry D., Coulhon T., Ledoux M., Saloff-Coste L. ( 1995), Sobolev inequalities in disguise, Indiana J. Math. 44 1034-1074. | Zbl | MR

Carlen E. ( 1991), Superadditivity of Fisher's information and logarithmic Sobolev inequalities, J. Funct. Anal. 101 194-211. | Zbl | MR

Carlen E., Kusuoka S., Stroock D. ( 1987), Upperbounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré 23 245-287. | Zbl | MR | Numdam

Carlen E., Loos M. ( 1993), Sharp constant in Nash's inequality. Duke Math. J., International Math. Research Notices 7 213-215. | Zbl

Carlen E., Loos M. ( 1995), Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier- Stokes equation, Duke Math. J. 81 135-157. | Zbl | MR

Chavel I. ( 1993), Riemannian geometry : a modern introduction, Cambridge Univ. Press. | Zbl | MR

Davies E. B. ( 1989), Heat kernels and spectral theory, Cambridge Univ. Press. | Zbl | MR

Gross L. ( 1975), Logarithmic Sobolev inequalities, Amer. J. Math. 97 1061-1083. | Zbl | MR

Kavian O., Kerkyacharian G., Roynette ( 1993), Quelques remarques sur l'hypercontractivité, J. Funct. Anal. 111 155-196. | Zbl | MR

Li P. ( 1986), Large time behavior of the heat equation on complete manifolds with non-negative Ricci curvature, Ann. Math. 124 1-21. | Zbl | MR

Li P., Yau S.T. ( 1986), On the parabolic kernel of the Schrödinger operator, Acta Math. 156 153-201. | Zbl | MR

Lleb E. ( 1990), Gaussian kernels have only Gaussian maximizers, Invent. math. 102 179-208. | Zbl | MR

Rosen J. ( 1976), Sobolev inequalities for weight spaces and supercontractivity, Trans. Amer. Math. Soc. 22 367-376. | Zbl | MR

Varopoulos N. ( 1985), Hardy-Littlewood theory for semigroups. J. Funct. Anal. 63 240-260. | Zbl | MR