On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift

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1. [1] Bakry, D., Etude probabiliste des transformees de Riesz et de l'espace H1 sur les spheres, Sem. Prob. XVIII, Lecture Notes in Math.1059, 197-218, Springer, 1984. Zbl0571.60012MR770962
2. [2] Bakry, D., L'hypercontractivite et son utilisation en theorie des semi-groupes, Preprint, 1993. MR1307413
3. [3] Bakry, D. and Emery, M., Diffusions hypercontractives, Sem. Prob. XIX, Lecture Notes in Math.1123, 177-206, Springer, 1985. Zbl0561.60080MR889476
4. [4] Bakry, D. and Emery, M., Propaganda for Γ2, in From Local Times to Global Geometry, Control and Physics, 39-46, K. D. Elworthy (ed.), Longman Sci. Tech., 1986. Zbl0608.58043MR894521
5. [5] Bouleau, N. and Hirsh, F., Dirichlet Forms and Analysis on Wiener Space, Walter de Gruyter, 1991. Zbl0748.60046MR1133391
6. [6] Davis, E.B., Heat Kernels and Spectral Theory, Cambridge Univ. Press, 1989. Zbl0699.35006MR990239
7. [7] Dellacherie, C. and Meyer, P.A., Probabilites et Potentiel IV, Hermann, 1991. Zbl0323.60039MR488194
8. [8] Fukushima, M., Dirichlet Forms and Markov Processes, North Holland, 1980. Zbl0422.31007MR569058
9. [9] Gross, L., Logarithmic Sobolev inequalities, Amer. J. Math.97 (1975),1061-1083. Zbl0318.46049MR420249
10. [10] He, S.W.and Wang, J.G., Gaussian measures on white noise space, Preprint, 1993. MR1459368
11. [11] Hida, T., Kuo, H.H., Potthoff, J. and Streit, L., White Noise - An Infinite Dimensional Calculus, Kluwer Academic Publ., 1993. Zbl0771.60048MR1244577
12. [12] Ma, Z. and Röckner, M., An Introduction to Non-symmetric Dirichlet Forms , Springer, 1992. Zbl0826.31001
13. [13] Nelson, E., A quadratic interaction in two dimension, In Mathematical Theory of Elementary Particles, R. Goodman and I. Segal (eds.), M.I.T. Press, 1966. MR210416
14. [14] Nelson, E., The free Markov field, J. Funct. Anal.12(1973), 211-227. Zbl0273.60079MR343816
15. [15] Potthoff, J. and Streit, L., A characterization on Hida distribution, J. Funct. Anal.101(1991), 212-229. Zbl0826.46035MR1132316
16. [16] Potthoff, J. and Yan, J.A., Some results about test and generalized functionals of white noise, In Proc. Singapore Prob. Conf., L.H.Y. Chen et al (eds.), Walter de Gruyter, 1992. Zbl0765.60030MR1188716
17. [17] Qian, Z.M., On the Martin boundary of the Ornstein-Uhlenbeck operator on the white noise space, Preprint, 1993. 
18. [18] Röckner, M., On the parabolic Martin boundary of the Ornstein-Uhlenbeck operator on Wiener space, Ann. Prob. (1992), 1063-1085. Zbl0761.60067MR1159586
19. [19] Rothaus, O., Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities, J. Funct. Anal.64(1985), 296-313. Zbl0578.46028MR812396
20. [20] Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Academic Press, 1985. Zbl0401.47001MR751959
21. [21] Simon, B., The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974. Zbl1175.81146MR489552
22. [22] Yan J.A., Some recent developments in white noise analysis. In Probability and Statistics, A. Badrikian et al (eds.), World Scientific, 1993. 
23. [23] Yokoi, Y., Positive generalized functionals, Hiroshima Math. J.20(1990), 137-157. Zbl0714.60052MR1050432

1. Sheng-Wu He, Jia-Gang Wang, The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited