P. Acquistapace and B. Terreni, A unified approach to abstract linear non-autonomous parabolic equations, Rend. Sem. Mat. Univ. Padova, vol.78, pp.47-107, 1987.

W. Arendt, Semigroups and evolution equations : functional calculus, regularity and kernel estimates, Handbook of Differential Equations, pp.1-85, 2004.

S. Arendt and . Bu, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Mathematische Zeitschrift, vol.240, issue.2, pp.311-343, 2002.
DOI : 10.1007/s002090100384

W. Arendt and S. Bu, Tools for maximal regularity, Mathematical Proceedings of the Cambridge Philosophical Society, vol.134, issue.02, pp.317-336, 2003.
DOI : 10.1017/S0305004102006345

R. Arendt, S. Chill, C. Fornaro, and . Poupaud, L p -maximal regularity for nonautonomous evolution equations, p.preprint, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00293778

J. B. Baillon, Caractère borné de certains générateurs de semi-groupes linéaires dans les espaces de Banach, C. R. Acad. Sci. Paris Sér. A-B, vol.290, issue.16, pp.757-760, 1980.

A. [. Benedek, R. Calderon, and . Panzone, CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS, Proc. Natl. Acad. Sci. USA, pp.356-365, 1962.
DOI : 10.1073/pnas.48.3.356

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC220785

[. Cannarsa and V. Vespri, On maximal L p regularity for the abstract Cauchy problem, Boll. Un. Mat. Ital. B, vol.5, pp.165-175, 1986.

[. Coulhon and X. T. Duong, Maximal regularity and kernel bounds : observations on a theorem by Hieber and Prüss, Adv. Differ. Equ, vol.5, issue.1-3, pp.343-368, 2000.

[. Coulhon and D. Lamberton, Régularité L p pour leséquationsleséquations d'´ evolution, Séminaire d'Analyse Fonctionnelle, Publ. Math. Univ. Paris VII, vol.26, pp.155-165, 1984.

[. Prato and P. Grisvard, Sommes d'opérateurs linéaires etéquationsetéquations différentielles opérationnelles, J. Math. Pures Appl, vol.54, pp.305-387, 1975.

[. Denk, M. Hieber, and J. Prüss, Fourier Multipliers and Problems of Elliptic and Parabolic Type, Memoirs Amer, Math. Soc. Amer. Math. Soc, vol.166, 2003.

[. L. Duren, Theory of H p -spaces, 1970.

[. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 1999.
DOI : 10.1007/s002330010042

S. Monniaux, Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations, Proc. Amer, pp.1047-1053, 2000.

M. Hieber and J. Prüss, Heat kernels and maximal L p ? L q estimates for parabolic evolution equations, Commun. Partial Diff. Eq, vol.22, pp.1647-1669, 1997.

[. Kalton and G. Lancien, A solution to the problem of $L^p-$maximal regularity, Mathematische Zeitschrift, vol.235, issue.3, pp.559-568, 2000.
DOI : 10.1007/PL00004816

[. Kalton and L. Weis, The $H^{\infty}-$ calculus and sums of closed operators, Mathematische Annalen, vol.321, issue.2, pp.319-345, 2001.
DOI : 10.1007/s002080100231

[. C. Kunstmann and L. Weis, Perturbation theorems for maximal L p -regularity, Ann. Scuola Norm. Sup. Pisa Cl. Sci, issue.4, pp.30-415, 2001.

[. C. Kunstmann and L. Weis, Maximal L p regularity for parabolic equations, Fourier multiplier theorems and H ? functional calculus, Levico Lectures, Proceedings of the Autumn School on Evolution Equations and Semigroups, pp.65-320, 2004.
DOI : 10.1007/978-3-540-44653-8_2

[. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Progress in Nonlinear Differential Equations and Their Applications, 1995.

[. Monniaux and A. Rhandi, Semigroup Methods to Solve Non-autonomous Evolution Equations, Semigroup Forum, vol.60, issue.1, pp.122-134, 2000.
DOI : 10.1007/s002330010006

J. Prüss and R. Schnaubelt, Solvability and Maximal Regularity of Parabolic Evolution Equations with Coefficients Continuous in Time, Journal of Mathematical Analysis and Applications, vol.256, issue.2, pp.405-430, 2001.
DOI : 10.1006/jmaa.2000.7247

[. E. Sobolevskii, Coerciveness inequalities for abstract parabolic equations, Dokl. Akad. Nauk SSSR, vol.157, pp.52-55, 1964.

L. De-cwikel-lieb-rozenblum and L. , inégalité de Cwikel-Lieb-Rozenblum donne une majoration du nombre de valeurs propres négatives de l'opérateur de Schrödinger ?? ? V sur L 2 (R n ), n ? 3. On considère un potentiel V ? 0 appartenantàappartenantà L n

W. Arendt and C. J. Batty, The spectral function and principal eigenvalues for Schrödinger operators. Potential Anal, pp.415-436, 1997.

T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, 1982.
DOI : 10.1007/978-1-4612-5734-9

A. Baider, Noncompact Riemannian manifolds with discrete spectra, Journal of Differential Geometry, vol.14, issue.1, pp.41-57, 1979.
DOI : 10.4310/jdg/1214434850

R. Brooks, A relation between growth and the spectrum of the Laplacian, Mathematische Zeitschrift, vol.14, issue.4, pp.501-508, 1981.
DOI : 10.1007/BF01174771

R. Brooks, On the spectrum of non-compact manifolds with finite volume, Mathematische Zeitschrift, vol.46, issue.3, pp.425-432, 1984.
DOI : 10.1007/BF01161957

J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, Journal of Differential Geometry, vol.17, issue.1, pp.15-53, 1982.
DOI : 10.4310/jdg/1214436699

S. Cheng, Eigenvalue comparison theorems and its geometric applications, Mathematische Zeitschrift, vol.9, issue.3, pp.289-297, 1975.
DOI : 10.1007/BF01214381

E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Tracts in Math, vol.92, 1989.
DOI : 10.1017/CBO9780511566158

[. Ii and E. B. Davies, Spectral Theory and Differential Operators. Cambridge Studies in Ad, Math, p.42, 1995.

[. Ii and J. Dodziuk, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math. J, vol.32, pp.703-716, 1983.

H. Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology, vol.20, issue.1, pp.1-14, 1981.
DOI : 10.1016/0040-9383(81)90012-4

[. Ii, H. Donnelly, and P. Li, Pure point spectrum and negative curvature for non-compact manifolds. Duke Math, J, vol.46, pp.497-503, 1979.

D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, 1987.

[. Ii, D. Gilbarg, and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 1983.

[. Ii, P. Hess, and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations, vol.5, pp.999-1030, 1980.

[. Ii and D. Jerison, The Poincaré inequality for vector fields satisfying Hörmander's condition . Duke Math, J, vol.53, pp.503-523, 1986.

V. Shubin and M. , Discreteness of spectrum for the Schrödinger operators on manifolds with bounded geometry, Oper. Theory Adv. Appl, vol.18, issue.110, pp.185-226, 1999.

[. Ii, D. Levin, and M. Solomyak, The Rozenblum-Lieb-Cwikel inequality for Markov generators, J. Anal. Math, vol.71, pp.173-193, 1997.

[. Ii and E. H. Lieb, Bounds on the eigenvalues of the Laplace and Schrödinger operators, Bull. Am. Math. Soc, vol.82, pp.751-753, 1976.

[. Ii, P. Maheux, and L. Saloff-coste, Analyse sur les boules d'un opérateur sous-elliptique, Math. Ann, vol.303, pp.713-740, 1995.

[. Ii, V. G. Maz-'ya, and I. E. Verbitsky, The Schrödinger operator on the energy space : Boundedness and compactness criteria, Acta Math, vol.188, pp.263-302, 2002.

[. Ii, G. Metafune, and D. Pallara, Discreteness of the spectrum for some differential operators with unbounded coefficients in R N, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Natur, vol.11, pp.9-19, 2000.

[. Ii, G. Metafune, and D. Pallara, On the localization of the essential spectrum of Schrödinger operators, Proc. Amer, pp.1779-1786, 2002.

[. Ii, S. Nayatani, and H. Urakawa, Spectrum of the Schrödinger operator on a complete manifold, J. Funct. Anal, vol.112, pp.459-479, 1993.

[. Ii and E. M. Ouhabaz, The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds. Duke Math, J, vol.110, pp.1-35, 2001.

[. Ii and E. M. Ouhabaz, Analysis of heat equations on domains, 2005.

[. Ii, E. M. Ouhabaz, and C. Poupaud, CLR-type estimates for Schrödinger operators on Riemannian manifolds

[. Ii and C. Poupaud, On the essential spectrum of Schrödinger operators on Riemannian manifolds, Math. Z, vol.251, pp.1-20, 2005.

M. Simon and B. , Methods of Modern Mathematical Physics. II : Fourier Analysis , Self-adjointness, 1975.

M. Simon and B. , Methods of Modern Mathematical Physics. IV : Analysis of Operators, 1978.

[. Ii and G. V. Rozenblum, The distribution of the discrete spectrum for singular differential operators, Sov. Math., Dokl. Dokl. Akad. Nauk SSSR, vol.13, issue.202, pp.245-249, 1972.

G. Rozenblum and M. Solomyak, CLR-estimate for the generators of positivity preserving and positively dominated semi-groups) ; translation from Algebra Anal, St. Petersbg. Math. J, vol.9, issue.96, pp.1195-1211, 1997.

L. Saloff-coste, A note on Poincaré, Sobolev, and Harnack inequalities, Internat. Math. Res. Notices, vol.34, pp.27-38, 1992.

[. Ii and Z. Shen, The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds, Proc. Amer, pp.3447-3456, 2003.

E. M. Stein, Harmonic Analysis : Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Mathematical Series 43, 1993.