Herbst inequalities for supercontractive semigroups

Kyoto Journal of Mathematics

Volumn 38, Issue 2, 1998, Pages 295-318

  Gross, Leonard ^a   Rothaus, Oscar ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032267704     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250518120     Document Type: Article

References (28)

1. S. Aida, T. Masuda and I. Shigekawa, Logarithmic Sobolev Inequalities and Exponential Integrability, J. of Funct. Anal., 126 (1994), 83-101.
2. S. Aida and I. Shigekawa, Logarithmic Sobolev inequalities and spectral gaps: perturbation theory, J. of Funct. Anal., 126 (1994), 448-475.
3. S. Aida and D. Stroock, Moment estimates derived from Poincare and logarithmic Sobolev inequalities, Math. Res. Lett., 1 (1994), 75-86.
4. S. Bobkov and M. Ledoux, Poincare's inequalities and Talagrand's concentration phenomenon for the exponential distribution, Probab. Theory and Related Fields, 107 (1997), 383-400.
5. R. Banuelos, Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators, J. of Funct. Anal, 100 (1991), 181-206.
6. R. Carmona, Regularity properties of Schrödinger and Dirichlet semigroups, J. of Funct. Anal, 33 (1979), 259-296.
7. Z-Q. Chen and R. Song, Intrinsic ultracontractivity and conditional gauge for symmetric stable processes, Cornell preprint, December, 1996 J. of Funct. Anal., to appear.
8. Thierry. Coulhon, Ultracontractivity and Nash type inequalities, J. of Funct. Anal., 141 (1996), 510-539.
9. R. Courant and D. Hilbert, Methematical Physics, vol.1, Interscience Publ., New York, 1953.
10. E.B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, 1989, pp. 197.
11. E.B Davies and B.Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. of Funct. Anal, 59 (1984), 335-395.
12. Burgess. Davis, Intrinsic ultracontractivity and the Dirichlet Laplacian, J. of Funct. Anal, 100 (1991), 162-180.
13. P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequalities for finite Markov chains, Ann. of Applied Probablity, 6 (1996), 695-750.
14. P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithm?, J. of Computational and Statistical sxience, To appear.
15. Leonard. Gross, Logarithmic Sobolev inequalities, Amer. J. of Math, 97 (1975), 1061-1083.
16. Leonard. Gross, Logarithmic Sobolev inequalities and contractive properties of semigroups, in "Dirichlet Forms", G.Dell'Antonio and U. Mosco, Eds., Varenna 1992, Lecture Notes in Mathematics, 1563, Springer-Verlag, Berlin 1993., pp. 54-88.
17. Ira. Herbst, Personal communication (November, 1975).
18. M. Hino, Spectral properties of Laplacians on an abstract Wiener space with a weighted Wiener measure, J. of Funct. Anal., 147 (1997), 485-520.
19. C.G.J. Jacobi, Zur theorie der variations-rechnung und der differential-gleichungen, J. fur Mathematik von Crelle, 17 (1837), 68-82.
20. S. Kusuoka and D. Stroock, Some boundedness properties of certain stationary diffusion semigroups, J. Funct. Anal., 60 (1985), 243-264.
21. M. Ledoux, Remarks on Logarithmic Sobolev Constants, Exponential Integrability, and Estimates on the Diameter, J. Math. Kyoto Univ., 35 (1995), 211-220.
22. Z. Ma and M. Rockner, An introduction to the theory of (non-symmetric) Dirichlet forms, Springer, Berlin, 1992.
23. p norms, Proc. of AMS, to appear.
24. J. Rosen, Sobolev inequalities for weight spaces and supercontractivity, Trans. A.M.S. 222 (1976), 367-376.
25. A.S. Ustunel, Integrabilite exponentielle de fonctionnelles de Wiener, CRAS, Paris, Serie I 315 (1992), 279-282.
26. A.S. Ustunel, Some exponential moment inequalities for the Wiener functionals, J. of Funct. Anal., 136 (1996), 154-170.
27. A.S. Ustunel, Exponential tightness of Wiener functional, in "Stochastic Analysis and Related Topics", A.S. Ustunel, Ed., Stochastic Monographs, vol.8, Gordon and Breach, 1993.
28. A.C. Zaanen, Linear Analysis, North-Holland Publ. Co., Amsterdam, 1964.