Heat kernels of multiplicative perturbations: Hölder estimates and Gaussian lower bounds

Indiana University Mathematics Journal

Volumn 47, Issue 4, 1998, Pages 1481-1495

  Ouhabaz, El Maati ^a  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039938923     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1998.47.1582     Document Type: Article

References (20)

1. R. A. ADAMS, Sobolev Spaces, Academic Press, 1975
2. P. AUSCHER, Regularity theorems and heat kernels for elliptic operators, J. London Math. Soc. 54 (1996) 284-296.
3. d edition, 1992.
4. TH. COULHON, Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opératuers et applications, Potential Anal. 1 (1992) 343-353.
5. p spaces, in Semigroup Theory and Evolution Equations, Clément et al. (eds.), Marcel Dekker. Lectures in Pure and Appl. Math. Vol. 135 (1991), 93-99.
6. TH. COULHON, Espaces de Lipschitz et inégalités de Poincaré, J. Funct. Anal. 136 (1996), 81-113.
7. TH. COULHON AND A. GRIGORY'AN, On-diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1997), 133-199.
8. E. B. DAVIES, Heat Kernels and Spectral Theory, Cambridge Univ. Press (1989).
9. E. B. DAVIES, Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc.(2) 5 (1997), 105-125.
10. X. T. DUONG AND E. M. OUHABAZ, Complex multiplicative perturbations of elliptic operators: Heat kernel bounds and holomorphic functional calculus, Diff. Integ. Eq. (to appear).
11. X. T. DUONG AND D. W. ROBINSON, Semigroup kernels, Poisson bounds and holomorphic functional calculus, J. Funct. Analysis 142 (1996), 89-128.
12. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice Hall, New Jersey, 1964.
13. A. GRIGORY'AN, upper bounds of derivatives of the heat kernel on arbitrary complete manifold, J. Funct. Anal. 127 (1995), 363-389.
14. A. MCINTOSH AND A. NAHMOD, Heat kernel estimates and functional calculi of -bΔ, (Preprint 1996).
15. E. M. OUHABAZ, Semi-groupes sous-Markoviens engendrés par des opérateurs matriciels, Math. Ann. 296 (1993), 667-676.
16. E. M. OUHABAZ, Gaussian estimates and holomorphy of semigroups, Proc. Amer. Math. Soc. 123 (1995), 1465-1474.
17. P. LI AND S. T. YAU, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201.
18. L. SALOFF-COSTE, Analyse sur les groupes de Lie à croissance polynomiale, Arkiv för Mat. 28 (1990), 315-331.
19. L. SALOFF-COSTE, Parabolic Harnack inequality for divergence form second order differential operators, Pot. Analysis 4 (1995), 429-467.
20. N. TH. VAROPOULOS, L. Saloff-Coste and Th. Coulhon, Analysis and Geometry on Groups, Cambridge Univ. Press, 1992.