Hypercontractivity for perturbed diffusion semigroups
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 4, pp. 609-628. 
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     author = {Cattiaux, Patrick},
     title = {Hypercontractivity for perturbed diffusion semigroups},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {609--628},
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     number = {4},
     year = {2005},
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     url = {http://www.numdam.org/item/AFST_2005_6_14_4_609_0/}
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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] 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

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

[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

[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 | Zbl

[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 | Zbl

[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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

[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). | EuDML | Numdam | MR | Zbl

[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 | Zbl

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

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

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