G. Allain, Sur la repr??sentation des formes de Dirichlet, Annales de l???institut Fourier, vol.25, issue.3-4, pp.1-10, 1975.
DOI : 10.5802/aif.570

D. Bakry and L. , hypercontractivité et son utilisation en théorie des semigroupes , in Markov semigroups at Saint-Flour. Probability at Saint- Flour, pp.1-114

. D. Bcl, D. Bakry, M. Concordet, and . Ledoux, Optimal heat kernel bounds under logarithmic Sobolev inequalities, ESAIM Probab. Statist, vol.197, pp.391-407, 1995.

D. Bakry, I. Gentil, and M. Ledoux, Analysis and geometry of Markov diffusion operators, Bendikov, Symmetric stable semigroups on the infinite-dimensional torus, pp.13-39, 1995.
DOI : 10.1007/978-3-319-00227-9
URL : https://hal.archives-ouvertes.fr/hal-00929960

. D. Bm-]-a, P. Bendikov, and . Maheux, Nash type inequalities for fractional powers of non-negative self-adjoint operators, Trans. Amer. Math. Soc, vol.359, pp.3085-3097, 2007.

. A. Cks-]-e, S. Carlen, D. W. Kusuoka, and . Stroock, Upper bounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré Probab. Statist, vol.23, pp.245-287, 1987.

T. B. Coulhond-]-e and . Davies, Ultracontractivity and Nash Type Inequalities, Journal of Functional Analysis, vol.141, issue.2, pp.510-539, 1989.
DOI : 10.1006/jfan.1996.0140

. B. Ds-]-e, B. Davies, and . Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, Dirichlet forms and Markov processes Heat kernel and analysis on manifolds, AMS/IP Studies in Advanced Mathematics 47, pp.335-395, 1980.

. A. Gh, J. Grigor-'yan, and . Hu, Upper bounds of heat kernels on doubling space, Moscow Math, J, vol.14, pp.505-563, 2014.

L. Gross, Logarithmic Sobolev Inequalities, American Journal of Mathematics, vol.97, issue.4, pp.1061-1083, 1976.
DOI : 10.2307/2373688

L. Gross, Logarithmic Sobolev inequalities and contractivity properties of semigroups, Lecture Notes in Math, vol.96, issue.2, pp.54-88, 1992.
DOI : 10.1007/BFb0074091

G. [. Kavian, B. Kerkyacharian, and . Roynette, Some Remarks on Ultracontractivity, Journal of Functional Analysis, vol.111, issue.1, pp.155-196, 1993.
DOI : 10.1006/jfan.1993.1008

J. Kigami, Local Nash Inequality and Inhomogeneity of Heat Kernels, Proc. London Math, pp.525-544, 2004.
DOI : 10.1112/S0024611504014807

J. Nashs-]-l and . Saloff-coste, Continuity of solutions of parabolic and elliptic equations Analysis on compact Lie groups of large dimension and on connected compact groups, Amer. J. Math. Colloq. Math, vol.80, issue.118, pp.931-954, 1958.

. V. St-]-v, V. N. Sazonov, and . Tutubalin, Probability distributions on topological groups, Theor. Prob. Appl, vol.11, pp.1-45, 1966.

. [. Th, Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal, vol.63, pp.240-260, 1985.

. Vsc-]-n, . Th, L. Varopoulos, T. Saloff-coste, and . Coulhon, Analysis and geometry on groups, Cambridge Tracts in Mathematics, vol.100, 1992.

F. Wang, Functional Inequalities for Empty Essential Spectrum, Journal of Functional Analysis, vol.170, issue.1, pp.219-245, 2000.
DOI : 10.1006/jfan.1999.3516

F. Wang, Functional Inequalities, Markov Processes and Spectral Theory, 2004.