C. Ané and M. Ledoux, On logarithmic Sobolev inequalities for continuous time random walks on graphs. Probab. Theory Related Fields, pp.573-602, 2000.

D. Applebaum, Lévy processes and stochastic calculus, volume 93 of Cambridge Studies in Advanced Mathematics, 2004.

D. Bakry, L'hypercontractivit?? et son utilisation en th??orie des semigroupes, Lecture Notes in Math, vol.48, issue.n.2, pp.1-114, 1994.
DOI : 10.1007/978-3-642-96208-0

P. Biler and G. Karch, Generalized Fokker-Planck equations and convergence to their equilibria, Evolution Equations Propagation Phenomena, Global Existence, Influence of Non-Linearities, pp.307-318, 2001.
DOI : 10.4064/bc60-0-24

D. Chafa¨?chafa¨?, Entropies, convexity, and functional inequalities, On $\Phi $-entropies and $\Phi $-Sobolev inequalities, Journal of Mathematics of Kyoto University, vol.44, issue.2, pp.325-363, 2004.
DOI : 10.1215/kjm/1250283556

A. Cotsiolis and N. K. Tavoularis, On logarithmic Sobolev inequalities for higher order fractional derivatives, Comptes Rendus Mathematique, vol.340, issue.3, pp.205-208, 2005.
DOI : 10.1016/j.crma.2004.11.030

J. Droniou and C. Imbert, Fractal First-Order Partial Differential Equations, Archive for Rational Mechanics and Analysis, vol.24, issue.2, pp.299-331, 2006.
DOI : 10.1007/s00205-006-0429-2

URL : https://hal.archives-ouvertes.fr/hal-00004462

I. Gentil and C. Imbert, The lévy-fokker-planck equation: ?-entropies and convergence to equilibrium, 2008.

L. Gross, Logarithmic Sobolev Inequalities, American Journal of Mathematics, vol.97, issue.4, pp.1061-1083, 1975.
DOI : 10.2307/2373688

F. B. Weissler, Logarithmic Sobolev inequalities for the heat-diffusion semigroup, Transactions of the American Mathematical Society, vol.237, pp.255-269, 1978.
DOI : 10.1090/S0002-9947-1978-0479373-2

L. Wu, A new modified logarithmic Sobolev inequality for Poisson point processes and several applications. Probab. Theory Related Fields, pp.427-438, 2000.