Hypercontractivity for perturbed diffusion semigroups
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 14 (2005) no. 4, p. 609-628
@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},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {4},
     year = {2005},
     pages = {609-628},
     zbl = {1089.60520},
     mrnumber = {2188585},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_4_609_0}
}
Cattiaux, Patrick. Hypercontractivity for perturbed diffusion semigroups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 14 (2005) no. 4, pp. 609-628. http://www.numdam.org/item/AFST_2005_6_14_4_609_0/

[1] Aida (S.). - An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups, J. Func. Anal. 185, p. 474-526 (2001). | Zbl 1038.60077

[2] Aida (S.) , Shigekawa ( I.). - Logarithmic Sobolev inequalities and spectral gaps: perturbation theory, J. Func. Anal. 126, p. 448-475 (1994). | MR 1305076 | Zbl 0846.46019

[3] Ané (C. ) , Blachère ( S.), Chafai (D.), Fougères (P.), Gentil (I.), Malrieu (F.), Roberto (C.), Scheffer (G.).- Sur les inégalités de Sobolev logarithmiques, volume 10 of Panoramas et Synthèses. S.M.F, Paris (2000). | Zbl 0982.46026

[4] Bakry (D.). - 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 1307413 | Zbl 0856.47026

[5] Barthe (F. ), Cattiaux (P.), Roberto (C.). - Interpolated inequalities between exponential and gaussian, Orlicz hypercontractivity and application to isoperimetry, Preprint (2004).

[6] Cattiaux ( P.). - A pathwise approach of some classical inequalities, Potential Analysis 20, p. 361-394 (2004). | MR 2032116 | Zbl 1050.47041

[7] Cattiaux ( P.), Léonard (C.) . - Minimization of the Kullback information for general Markov processes. Séminaire de Probas XXX, Lect. Notes Math 1626, p. 283-311 (1996). | Numdam | Zbl 0863.60073

[8] Davies (E.B. ). - Heat kernels and spectral theory , Cambridge University Press (1989 ). | MR 990239 | Zbl 0699.35006

[9] Deuschel (J.D. ), Stroock (D.W.). - Large deviations, Academic Press (1989). | MR 997938 | Zbl 0705.60029

[10] Gong (F.Z. ), Wu ( L.M.).- Spectral gap of positive operators and its applications, C. R. Acad. Sci. Paris, Sér. 1, t 331, p. 983-988 (2000). | MR 1809440 | Zbl 0984.47030

[11] Gross (L.). - 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 1292277 | Zbl 0812.47037

[12] Guionnet ( A.), Zegarlinski (B.).- Lectures on logarithmic Sobolev inequalities, Séminaire de Probabilités XXXVI, Lect. Notes Math 1801, (2002). | Numdam | MR 1971582 | Zbl 1125.60111

[13] Kavian (O. ), Kerkyacharian (G.), Roynette (B.).- Quelques remarques sur l'ultracontractivité, J. Func. Anal. 111, p. 155-196 (1993). | MR 1200640 | Zbl 0807.47027

[14] Kunz (A.). - On extremes of multidimensional stationary diffusion processes in euclidean norm, Preprint (2002).

[15] Kusuoka ( S.), Stroock (D.). - Some boundedness properties of certain stationary diffusion semigroups, J. Func. Anal. 60, p. 243-264 (1985). | MR 777238 | Zbl 0562.60078

[16] Ledoux (M. ). - Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probas XXXIII, Lect. Notes Math 1709, p. 120-216 (1999). | Numdam | MR 1767995 | Zbl 0957.60016

[17] Mathieu ( P.). - Quand l'inégalité Log-Sobolev implique l'inégalité de trou spectral, Séminaire de Probas XXXII, Lect. Notes Math 1686, p. 30-35 (1998). | Numdam | MR 1651227 | Zbl 0913.60072

[18] Röckner ( M.), Wang (F.Y.). - Weak Poincaré inequalities and L2 convergence rates of Markov semigroups, J. Func. Anal. 185 , p. 564-603 (2001). | MR 1856277 | Zbl 1009.47028

[19] Rosen (J. ).- Sobolev inequalities for weight spaces and supercontractivity, Trans. Amer. Math. Soc. 222, p. 367-376 (1976). | MR 425601 | Zbl 0344.46072

[20] Royer (G.). - Une initiation aux inégalités de Sobolev logarithmiques , S.M.F., Paris ( 1999). | MR 1704288 | Zbl 0927.60006

[21] Wang (F.Y. ).- Logarithmic Sobolev inequalities: conditions and counterexamples, J. Operator Theory 46, p. 183-197 (2001). | MR 1862186 | Zbl 0993.58019