On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift

Zhongmin Qian; Sheng-Wu He

Séminaire de probabilités de Strasbourg (1995)

  • Volume: 29, page 202-217

How to cite


Qian, Zhongmin, and He, Sheng-Wu. "On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift." Séminaire de probabilités de Strasbourg 29 (1995): 202-217. <http://eudml.org/doc/113903>.

author = {Qian, Zhongmin, He, Sheng-Wu},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {hypercontractivity; Ornstein-Uhlenbeck semigroup; white noise analysis},
language = {fre},
pages = {202-217},
publisher = {Springer - Lecture Notes in Mathematics},
title = {On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift},
url = {http://eudml.org/doc/113903},
volume = {29},
year = {1995},

AU - Qian, Zhongmin
AU - He, Sheng-Wu
TI - On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift
JO - Séminaire de probabilités de Strasbourg
PY - 1995
PB - Springer - Lecture Notes in Mathematics
VL - 29
SP - 202
EP - 217
LA - fre
KW - hypercontractivity; Ornstein-Uhlenbeck semigroup; white noise analysis
UR - http://eudml.org/doc/113903
ER -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.