L. Ambrosio and S. Rigot, Optimal mass transportation in the Heisenberg group, Journal of Functional Analysis, vol.208, issue.2, pp.261-301, 2004.
DOI : 10.1016/S0022-1236(03)00019-3

H. Bahouri and J. , Equations d'ondes quasilineaires et estimations de Strichartz, American Journal of Mathematics, vol.121, issue.6, pp.1337-1377, 1999.
DOI : 10.1353/ajm.1999.0038

H. Bahouri and I. Gallagher, Paraproduit sur le groupe de Heisenberg et applications, Revista Matem??tica Iberoamericana, vol.17, pp.69-105, 2001.
DOI : 10.4171/RMI/289

H. Bahouri and I. Gallagher, The Heat Kernel and Frequency Localized Functions on the Heisenberg Group, Progress in nonlinear differential equations and their applications
DOI : 10.1007/978-0-8176-4861-9_2

URL : https://hal.archives-ouvertes.fr/hal-00269201

H. Bahouri, P. Gérard, and C. Xu, Espaces de Besov et estimations de Strichartz g??n??ralis??es sur le groupe de Heisenberg, Journal d'Analyse Math??matique, vol.42, issue.1, pp.93-118, 2000.
DOI : 10.1007/BF02791223

R. Beals, Weighted distribution spaces and pseudodifferential operators, Journal d'Analyse Math??matique, vol.245, issue.2, pp.130-187, 1981.
DOI : 10.1007/BF02803334

R. Beals and P. Greiner, Calculus on Heisenberg manifolds, Annals of Mathematics Studies, vol.119, 1988.

R. Beals, B. Gaveau, P. Greiner, and J. Vauthier, The Laguerre Calculus on the Heisenberg Group, II. Bulletin des Sciences Mathmatiques, vol.110, issue.23, pp.225-288, 1986.
DOI : 10.1007/978-94-010-9787-1_5

J. Bergh and J. Löfström, Interpolation spaces, an introduction, 1976.

I. Birindelli and E. Valdinoci, THE GINZBURG???LANDAU EQUATION IN THE HEISENBERG GROUP, Communications in Contemporary Mathematics, vol.10, issue.05, pp.671-719, 2008.
DOI : 10.1142/S0219199708002946

J. Bony, Calcul symbolique et propagation des singularités pour leséquationsleséquations aux dérivées partielles non linéaires, pp.209-246, 1981.

J. Bony and J. Chemin, Espaces fonctionnels associés au cacul de Weyl-Hörmander, pp.77-118, 1994.

J. Bony and N. Lerner, Quantification asymptotique et microlocalisation d'ordre supérieur, Annales de l' ´ Ecole Normale Supérieure, pp.377-433, 1989.

W. Brockett, Control Theory and Singular Riemannian Geometry, New Directions in Applied Mathematics, p.1127, 1981.
DOI : 10.1007/978-1-4612-5651-9_2

A. P. Calderón and R. Vaillancourt, On the boundedness of pseudo-differential operators, Journal of the Mathematical Society of Japan, vol.23, issue.2, pp.374-378, 1971.
DOI : 10.2969/jmsj/02320374

C. E. Cancelier, J. Chemin, and C. Xu, Calcul de Weyl-Hörmander et opérateurs sous-elliptiques, Annales de l'Institut Fourier, pp.43-1157, 1993.
DOI : 10.5802/aif.1367

URL : http://archive.numdam.org/article/AIF_1993__43_4_1157_0.pdf

L. Capogna, D. Danielli, S. D. Pauls, and J. T. Tyson, An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Progress in Mathematics, vol.259, 2007.

J. Chemin and C. Xu, Inclusions de sobolev en calcul de weyl-h??rmander et champs de vecteurs sous-elliptiques, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.30, issue.6, pp.719-751, 1997.
DOI : 10.1016/S0012-9593(97)89937-5

R. Coifman and Y. Meyer, Audeì a des opérateurs pseudo-différentiels, Astérisque 57, 1978.

S. Coré and D. Geller, Hörmander type pseudodifferential calculus on homogeneous groups, prépublication, 2008.

L. Corwin and F. Greenleaf, Representations of nilpotent Lie groups and their applications Part I. Basic theory and examples, Cambridge Studies in Advanced Mathematics, 1990.

M. Dimassi and J. Sjöstrand, Spectral asymptotics in the semi-classical limit, 1999.
DOI : 10.1017/CBO9780511662195

E. Van-erp, The Atiyah-Singer index formula for subelliptic operators on contact manifolds , Part I, 2008.

E. Van-erp, The Atiyah-Singer index formula for subelliptic operators on contact manifolds, Part II, 2008.

E. Van-erp, The index of hypoelliptic operators on foliated manifolds, Journal of Noncommutative Geometry, 2008.
DOI : 10.4171/JNCG/71

J. Faraut and K. Harzallah, Deux cours d'analyse harmonique, ´ Ecole d' ´ Eté d'analyse harmonique de Tunis, 1984.

J. Faraut and L. Sall, Wigner semi-circle law and Heisenberg group, Noncommutative harmonic analysis with applications to probability, Polish Academy Sciences, pp.133-143, 2007.

R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, International Series in Pure and Applied Physics, 1965.

C. Fermanian, Semi-classical analysis of generic codimension 3 crossings, International Mathematics Resarch Notices, vol.45, pp.2391-2435, 2004.

G. B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, 1989.

B. Franchi, S. Gallot, and R. I. , Sobolev and isoperimetric inequalities for degenerate metrics, Mathematische Annalen, vol.86, issue.IV, pp.557-571, 1994.
DOI : 10.1007/BF01450501

B. Franchi and E. Lanconelli, Une métrique associéè a une classe d'opérateurs elliptiques dégénérés, proceedings of the meeting Linear partial and Pseudo differential operators, Special Issue, pp.105-114, 1983.

G. Furioli, C. Melzi, and A. Veneruso, Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group, Journal canadien de math??matiques, vol.59, issue.6, pp.1301-1322, 2007.
DOI : 10.4153/CJM-2007-056-1

G. Furioli and A. Veneruso, Strichartz inequalities for the Schr??dinger equation with the full Laplacian on the Heisenberg group, Studia Mathematica, vol.160, issue.2, pp.157-178, 2004.
DOI : 10.4064/sm160-2-4

N. Garofalo and D. Vassilev, Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups, Mathematische Annalen, vol.318, issue.3, pp.453-516, 2000.
DOI : 10.1007/s002080000127

B. Gaveau, P. Greiner, and J. Vauthier, Int??grales de Fourier quadratiques et calcul symbolique exact sur le groupe d'Heisenberg, Journal of Functional Analysis, vol.68, issue.2, pp.248-272, 1986.
DOI : 10.1016/0022-1236(86)90006-6

URL : http://doi.org/10.1016/0022-1236(86)90006-6

D. Geller, Analytic pseudodifferential operators for the Heisenberg group and local solvability, Mathematical Notes, vol.37, 1990.
DOI : 10.1515/9781400860739

P. Gérard, Microlocal defect measures, Communications in Partial Differential Equations, vol.114, issue.11, pp.1761-1794, 1991.
DOI : 10.1080/03605308508820384

P. Gérard, P. Markowich, N. Mauser, and &. F. Poupaud, Homogenization limits and Wigner transforms, Communications on Pure and Applied Mathematics, vol.50, issue.4, pp.323-379, 1997.
DOI : 10.1002/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.3.CO;2-Q

P. Greiner, On the Laguerre calculus of left-invariant convolution (pseudodifferential) operators on the Heisenberg group, Goulaouic-Meyer-Schwartz Seminar, 1980.

A. Grossmann, G. Loupias, and E. Stein, An algebra of pseudodifferential operators and quantum mechanics in phase space, Annales de l'Institut Fourier, pp.343-368, 1968.

L. Hörmander, The analysis of linear partial differential equations, 1985.

A. Hulanicki, A functional calculus for Rockland operators on nilpotent Lie groups, Studia Mathematica, vol.78, pp.253-266, 1984.

S. Klainerman and I. Rodnianski, A geometric approach to the Littlewood-Paley theory, Geometric and Functional Analysis, pp.126-163, 2006.

P. Lemarié-rieusset, Base d'ondelettes sur les groupes de Lie stratifiés, pp.211-232, 1989.

N. Lerner, Metrics on the Phase Space and Non-Selfadjoint Operators

Y. Manin, Theta functions, quantum tori and Heisenberg groups, Letters in Mathematical Physics, vol.56, issue.3, pp.295-320, 2001.
DOI : 10.1023/A:1017909525397

A. Melin, Parametrix constructions for some classes of right-invariant differential operators on the heisenberg group, Communications in Partial Differential Equations, vol.240, issue.11, pp.1363-1405, 1981.
DOI : 10.1080/03605308108820214

D. Müller and E. Stein, $L^p$-estimates for the wave equation on the Heisenberg group, Revista Matem??tica Iberoamericana, vol.15, issue.2, pp.297-334, 1999.
DOI : 10.4171/RMI/258

A. I. Nachman, The wave equation on the heisenberg group, Communications in Partial Differential Equations, vol.24, issue.4, pp.675-714, 1982.
DOI : 10.1080/03605308208820236

M. Reed and B. Simon, Methods of Modern Mathematical Physics, Functional Analysis

S. Rigot, Transport de masse optimal et géométrie sous-riemannienne: le cas du groupe de Heisenberg (French) [Optimal mass transport and sub-Riemannian geometry: the case of the Heisenberg group] Séminaire: ´ Equations aux Dérivées Partielles, Exposé No: XIX, Séminairé Equations aux Dérivées Partielles, Ecole Polytechnique, 2006.

D. Robert, Autour de l'approximation semi?classique, 1983.

L. Rothschild and E. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Mathematica, vol.137, issue.0, pp.247-320, 1977.
DOI : 10.1007/BF02392419

M. Ruzhansky and V. Turunen, On the Fourier analysis of operators on the torus. Modern trends in pseudodifferential operators, Operator Theory, Analysis and Mathematical Physics, vol.172, pp.87-105, 2007.

M. Sato, T. Kawai, and M. Kashiwara, Microfunctions and pseudo-differential equations. Hyperfunctions and pseudo-differential equations, Proc. Conference Katata, pp.287-265, 1971.

M. Sato, T. Kawai, and M. Kashiwara, The theory of pseudodifferential equations in the theory of hyperfunctions, Collection of articles on hyperfunctions Sûgaku, pp.25-213, 1973.

E. M. Stein, Harmonic Analysis, 1993.

M. E. Taylor, Noncommutative Harmonic Analysis, Mathematical Surveys and Monographs, 1986.

S. Thangavelu, Harmonic Analysis on the Heisenberg group, Progress in Mathematics, p.159, 1998.
DOI : 10.1007/978-1-4612-1772-5

R. Tolimieri, The theta transform and the Heisenberg group, Journal of Functional Analysis, vol.24, issue.4, pp.353-363, 1977.
DOI : 10.1016/0022-1236(77)90063-5

A. Unterberger, Oscillateur harmonique et opérateurs pseudo-différentiels, Annales de l' Institut de Fourier, pp.201-221, 1979.

C. Xu, Propagation au bord des singularit??s pour des probl??mes de Dirichlet non lin??aires d'ordre deux, Journal of Functional Analysis, vol.92, issue.2, pp.325-347, 1990.
DOI : 10.1016/0022-1236(90)90054-O

C. Xu and C. Zuily, Higher interior regularity for quasilinear subelliptic systems, Calculus of Variations and Partial Differential Equations, vol.5, issue.4, pp.323-343, 1997.
DOI : 10.1007/s005260050069

J. Zienkiewicz, Schr??dinger equation on the Heisenberg group, Studia Mathematica, vol.161, issue.2, pp.99-111, 2004.
DOI : 10.4064/sm161-2-1

C. Zuily, Existence globale de solutionsrégulì eres pour l'´ equation des ondes non linéaire amortie sur le groupe de Heisenberg (French) [Global existence of regular solutions for the damped nonlinear wave equation on the Heisenberg group, pp.323-360, 1993.