@article{AFST_2005_6_14_4_609_0, author = {Cattiaux, Patrick}, title = {Hypercontractivity for perturbed diffusion semigroups}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {609--628}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 14}, number = {4}, year = {2005}, mrnumber = {2188585}, zbl = {1089.60520}, language = {en}, url = {http://www.numdam.org/item/AFST_2005_6_14_4_609_0/} }
TY - JOUR AU - Cattiaux, Patrick TI - Hypercontractivity for perturbed diffusion semigroups JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2005 SP - 609 EP - 628 VL - 14 IS - 4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/item/AFST_2005_6_14_4_609_0/ LA - en ID - AFST_2005_6_14_4_609_0 ER -
%0 Journal Article %A Cattiaux, Patrick %T Hypercontractivity for perturbed diffusion semigroups %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2005 %P 609-628 %V 14 %N 4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/item/AFST_2005_6_14_4_609_0/ %G en %F AFST_2005_6_14_4_609_0
Cattiaux, Patrick. Hypercontractivity for perturbed diffusion semigroups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 609-628. http://www.numdam.org/item/AFST_2005_6_14_4_609_0/
[1] An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups, J. Func. Anal. 185, p. 474-526 (2001). | Zbl
-[2] Logarithmic Sobolev inequalities and spectral gaps: perturbation theory, J. Func. Anal. 126, p. 448-475 (1994). | MR | Zbl
, -[3] Sur les inégalités de Sobolev logarithmiques, volume 10 of Panoramas et Synthèses. S.M.F, Paris (2000). | Zbl
, , , , , , , -[4] L'hypercontractivité et son utilisation en théorie des semi groupes, Ecole d'été de Probabilités de Saint-Flour. Lect. Notes Math 1581, p. 1-114 (1994). | MR | Zbl
-[5] Interpolated inequalities between exponential and gaussian, Orlicz hypercontractivity and application to isoperimetry, Preprint (2004).
, , -[6] A pathwise approach of some classical inequalities, Potential Analysis 20, p. 361-394 (2004). | MR | Zbl
-[7] Minimization of the Kullback information for general Markov processes. Séminaire de Probas XXX, Lect. Notes Math 1626, p. 283-311 (1996). | Numdam | Zbl
, . -[8] Heat kernels and spectral theory , Cambridge University Press (1989 ). | MR | Zbl
-[9] Large deviations, Academic Press (1989). | MR | Zbl
, -[10] Spectral gap of positive operators and its applications, C. R. Acad. Sci. Paris, Sér. 1, t 331, p. 983-988 (2000). | MR | Zbl
, -[11] Logarithmic Sobolev inequalities and contractivity properties of semi-groups, in Dirichlet forms, Dell'Antonio and Mosco eds, Lect. Notes Math 1563, p. 54-88 (1993). | MR | Zbl
-[12] Lectures on logarithmic Sobolev inequalities, Séminaire de Probabilités XXXVI, Lect. Notes Math 1801, (2002). | EuDML | Numdam | MR | Zbl
, -[13] Quelques remarques sur l'ultracontractivité, J. Func. Anal. 111, p. 155-196 (1993). | MR | Zbl
, , -[14] On extremes of multidimensional stationary diffusion processes in euclidean norm, Preprint (2002).
-[15] Some boundedness properties of certain stationary diffusion semigroups, J. Func. Anal. 60, p. 243-264 (1985). | MR | Zbl
, -[16] Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probas XXXIII, Lect. Notes Math 1709, p. 120-216 (1999). | EuDML | Numdam | MR | Zbl
-[17] Quand l'inégalité Log-Sobolev implique l'inégalité de trou spectral, Séminaire de Probas XXXII, Lect. Notes Math 1686, p. 30-35 (1998). | EuDML | Numdam | MR | Zbl
-[18] Weak Poincaré inequalities and L2 convergence rates of Markov semigroups, J. Func. Anal. 185 , p. 564-603 (2001). | MR | Zbl
, -[19] Sobolev inequalities for weight spaces and supercontractivity, Trans. Amer. Math. Soc. 222, p. 367-376 (1976). | MR | Zbl
-[20] Une initiation aux inégalités de Sobolev logarithmiques , S.M.F., Paris ( 1999). | MR | Zbl
-[21] Logarithmic Sobolev inequalities: conditions and counterexamples, J. Operator Theory 46, p. 183-197 (2001). | MR | Zbl
-