Optimal heat kernel bounds under logarithmic Sobolev inequalities

D. Bakry; D. Concordet; M. Ledoux

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 391-407
  • ISSN: 1292-8100

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Bakry, D., Concordet, D., and Ledoux, M.. "Optimal heat kernel bounds under logarithmic Sobolev inequalities." ESAIM: Probability and Statistics 1 (1997): 391-407. <http://eudml.org/doc/104241>.

@article{Bakry1997,
author = {Bakry, D., Concordet, D., Ledoux, M.},
journal = {ESAIM: Probability and Statistics},
keywords = {Riemannian manifold; functional inequalities; Markov semigroups; optimal uniform upper estimates; heat kernels; logarithmic Sobolev inequality; entropy-energy inequality; diffusion operators},
language = {eng},
pages = {391-407},
publisher = {EDP Sciences},
title = {Optimal heat kernel bounds under logarithmic Sobolev inequalities},
url = {http://eudml.org/doc/104241},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Bakry, D.
AU - Concordet, D.
AU - Ledoux, M.
TI - Optimal heat kernel bounds under logarithmic Sobolev inequalities
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 391
EP - 407
LA - eng
KW - Riemannian manifold; functional inequalities; Markov semigroups; optimal uniform upper estimates; heat kernels; logarithmic Sobolev inequality; entropy-energy inequality; diffusion operators
UR - http://eudml.org/doc/104241
ER -

References

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  3. BAKRY D., COULHON T., LEDOUX M., SALOFF-COSTE L. ( 1995), Sobolev inequalities in disguise, Indiana J. Math. 44 1034-1074. Zbl0857.26006MR1386760
  4. CARLEN E. ( 1991), Superadditivity of Fisher's information and logarithmic Sobolev inequalities, J. Funct. Anal. 101 194-211. Zbl0732.60020MR1132315
  5. CARLEN E., KUSUOKA S., STROOCK D. ( 1987), Upperbounds for symmetric Markov transition functions, Ann. Inst. H. Poincaré 23 245-287. Zbl0634.60066MR898496
  6. CARLEN E., LOOS M. ( 1993), Sharp constant in Nash's inequality. Duke Math. J., International Math. Research Notices 7 213-215. Zbl0822.35018
  7. CARLEN E., LOOS M. ( 1995), Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier- Stokes equation, Duke Math. J. 81 135-157. Zbl0859.35011MR1381974
  8. CHAVEL I. ( 1993), Riemannian geometry : a modern introduction, Cambridge Univ. Press. Zbl0810.53001MR1271141
  9. DAVIES E. B. ( 1989), Heat kernels and spectral theory, Cambridge Univ. Press. Zbl0699.35006MR990239
  10. GROSS L. ( 1975), Logarithmic Sobolev inequalities, Amer. J. Math. 97 1061-1083. Zbl0318.46049MR420249
  11. KAVIAN O., KERKYACHARIAN G., ROYNETTE ( 1993), Quelques remarques sur l'hypercontractivité, J. Funct. Anal. 111 155-196. Zbl0807.47027MR1200640
  12. LI P. ( 1986), Large time behavior of the heat equation on complete manifolds with non-negative Ricci curvature, Ann. Math. 124 1-21. Zbl0613.58032MR847950
  13. LI P., YAU S.T. ( 1986), On the parabolic kernel of the Schrödinger operator, Acta Math. 156 153-201. Zbl0611.58045MR834612
  14. LlEB E. ( 1990), Gaussian kernels have only Gaussian maximizers, Invent. math. 102 179-208. Zbl0726.42005MR1069246
  15. ROSEN J. ( 1976), Sobolev inequalities for weight spaces and supercontractivity, Trans. Amer. Math. Soc. 22 367-376. Zbl0344.46072MR425601
  16. VAROPOULOS N. ( 1985), Hardy-Littlewood theory for semigroups. J. Funct. Anal. 63 240-260. Zbl0608.47047MR803094

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