A generalization of poincaré and log-Sobolev inequalities

Potential Analysis

Volumn 22, Issue 1, 2005, Pages 1-15

  Wang, Feng Yu ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Concentration; Functional inequality; Markov semi group

Indexed keywords

EID: 15244346368     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11118-004-4006-8     Document Type: Article

References (30)

1. Aida, A., Masuda, T. and Shigekawa, I.: 'Logarithmic Sobolev inequalities and exponential integrability', J. Funct. Anal. 126 (1994), 83-101.
2. Aida, S. and Stroock, D.: 'Moment estimates derived from Poincaré and logarithmic Sobolev inequalities', Mat. Res. Lett. 1 (1994), 75-86.
3. Bakry, D.: L'hypercontractivite et Son Utilisation en Theorie des Semigroupes, Lecture Notes in Math. 1581, Springer-Verlag, 1994, pp. 1-114.
4. Bakry, D.: 'On Sobolev and logarithmic Sobolev inequalities for Markov semigroups', in New Trends in Stochastic Analysis, World Scientific, 1997, pp. 43-57.
5. Beckner, W.: 'A generalized Poincaré inequality for Gaussian measures', Proc. Amer. Math. Soc. 105 (1989), 397-400.
6. Bobkov, S.G. and Götz, F.: 'Exponential integrability and transportation cost related to logarithmic Sobolev inequalities', J. Funct. Anal. 163 (1999), 1-28.
7. Chafaï, D.: 'A note on Φ-entropies and Φ-Sobolev inequalities', in preparation.
8. Chavel, I.: Riemannian Geometry - A Modern Introduction, Cambridge Univ. Press, 1993.
9. Chen, M.F.: 'Variational formulas of Poincaré-type inequalities in Banach spaces of functions on the line', Acta Math. Sin. Eng. Ser. 18 (2002), 417-436.
10. Chen, M.-F. and Wang, F.-Y.: 'Estimates of logarithmic Sobolev constant: An improvement of Bakry-Emery criterion', J. Funct. Anal. 144 (1997), 287-300.
11. Deuschel, J.-D. and Stroock, D.W.: Large Deviations, Academic Press, New York, 1989.
12. Deuschel, J.-D. and Stroock, D.W.: 'Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models', J. Funct. Anal. 92 (1990), 30-48.
13. Donnely, H. and Li, P.: 'Lower bounds for the eigenvalues of Riemannian manifolds', Michigan Math. J. 29 (1982), 149-161.
14. Gong, F.-Z. and Wang, F.-Y.: 'Functional inequalities for uniformly integrable semigroups and application to essential spectrums', Forum Math. 12 (2002), 293-313.
15. ∞ approximations of convex, subharmonic, and plurisubharmonic functions', Ann. Sci. École Norm. Sup. (4) 12 (1979), 47-84.
16. Gross, L.: 'Logarithmic Sobolev inequalities', Amer. J. Math. 97 (1976), 1061-1083.
17. Gross, L.: 'Logarithmic Sobolev inequalities and contractivity properties of semigroups', in Lecture Notes in Math. 1563, Springer, 1993, pp. 54-88.
18. Gross, L. and Rothaus, O.: 'Herbst inequalities for supercontractive semigroups', J. Math. Kyoto Univ. 38 (1998), 295-318.
19. Holley, R. and Stroock, D.W.: 'Logarithmic Sobolev inequalities and stochastic Ising models', J. Statist. Phys. 46 (1987), 1159-1194.
20. Latała, R. and Oleszkiewicz, K.: 'Between Sobolev and Poincaré', in Lecture Notes in Math. 1745, 2000, pp. 147-168.
21. Ledoux, M.: 'On Talagrand's deviation inequalities for product measures', ESAIM: Probab. and Statist. 1 (1996), 63-87.
22. Ledoux, M.: 'Concentration of measures and logarithmic Sobolev inequalities', in Lecture Notes in Math. 1709, 1999, pp. 120-216.
23. Mao, Y.-H.: 'On empty essential spectrum for Markov processes in dimension one', Preprint.
24. 2-convergence rates of Markov semigroups', J. Funct. Anal. 185 (2001). 564-603.
25. Röckner, M. and Wang, F.-Y.: 'On the spectrum of a class of nonsectorial diffusion operators', Bull. Lond. Math. Soc. 36 (2004), 95-104.
26. Stroock, D.W.: An Introduction to the Theory of Large Deviations, Universitext, Springer-Verlag, 1984.
27. Wang, F.-Y.: 'Existence of the spectral gap for elliptic operators', Ark. Mat. 37 (1999), 395-407.
28. Wang, F.-Y.: 'Functional inequalities for empty essential spectrum', J. Funct. Anal. 170 (2000), 219-245.
29. Wang, F.-Y.: 'Functional inequalities, semigroup properties and spectrum estimates', Infin. Dimens. Anal. Quant. Probab. Rel. Topics 3 (2000), 263-295.
30. Wang, F.-Y.: 'Sobolev type inequalities for general symmetric forms', Proc. Amer. Math. Soc. 128 (2000), 3675-3682.