H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr, vol.186, pp.5-56, 1997.

M. Atiyah and I. Singer, The Index of Elliptic Operators on Compact Manifolds, Bull. Amer. Math. Soc, vol.69, pp.422-433, 1963.

J. Bergh and J. Löfström, Interpolation Spaces: An Introduction, 1976.

G. Bourdaud, Une algèbre maximale d'opérateurs pseudo-différentiels de type 1,1. Séminaire sur les Équations aux Dérivées Partielles, Exp. No. VII, 17 pp., École Polytech, 1987.

A. P. Calderón and R. Vaillancourt, A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A, vol.69, pp.1185-1187, 1972.

Z. Chen, Q. Xu, and Z. Yin, Harmonic analysis on quantum tori, Comm. Math. Phys, vol.322, issue.3, pp.755-805, 2013.

R. Coifman and Y. Meyer, Au delá des operateurs pseudo-différentiels, 1978.

R. Coifman, Y. Meyer, and E. M. Stein, Some new function spaces and their applications to Harmonic analysis, J. Funct. Anal, vol.62, issue.2, pp.304-335, 1985.

R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc, vol.83, issue.4, pp.569-645, 1977.

J. Conde, A note on dyadic coverings and nondoubling Calderón-Zygmund theory, J. Math. Anal. Appl, vol.397, pp.785-790, 2013.

A. Connes, C. R. Acad. Sci. Paris Sér. A-B, vol.290, issue.13, pp.599-604, 1980.

A. Connes, Noncommutative Geometry, 1994.

R. E. Edwards and G. I. Gaudry, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.90, 1977.

C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math, vol.129, issue.3-4, pp.137-193, 1972.

M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J, vol.34, issue.4, pp.777-799, 1985.

M. Frazier and B. Jawerth, The ?-transform and applications to distribution spaces, Function spaces and applications, vol.1302, pp.223-246, 1988.

M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal, vol.93, issue.1, pp.34-170, 1990.

M. Frazier, R. Torres, and G. Weiss, The boundedness of Calderón-Zygmund operators on the spaces ? F ?,q p, Rev. Mat. Iberoam, vol.4, pp.41-72, 1988.

J. García-cuerva and J. L. Rubio-de-francia, Weighted norm inequalities and related topics. North-Holland Mathematics Studies, 116. Notas de Matemática, vol.104, 1985.

J. B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol.96, 1981.

D. Goldberg, A local version of real Hardy spaces, Duke Math. J, vol.46, issue.1, pp.27-42, 1979.

A. M. González-pérez, M. Junge, and J. Parcet, Singular integral in quantum Euclidean spaces

L. Grafakos, Classical Fourier analysis. Second Edition, 2008.

G. Hong, L. D. López-sánchez, J. M. Martell, and J. Parcet, Calderón-Zygmund operator associated to matrix-valued kernels, Int. Math. Res. Not, issue.5, pp.1221-1252, 2014.

L. Hörmander, Pseudo-differential operators, vol.18, pp.501-517, 1965.

L. Hörmander, Pseudo-differential operators and hypoelliptic equations. Singular integrals. (Proc. Sympos, pp.138-183, 1966.

T. Hytönen, The real-variable Hardy space and BMO. Lecture notes of a course at the University of Helsinki, 2010.

M. Junge, Doob's inequality for non-commutative martingales, J. Reine Angew. Math, vol.549, pp.149-190, 2002.

M. Junge and M. Musat, A noncommutative version of the John-Nirenberg theorem, Trans. Amer. Math. Soc, vol.359, issue.1, pp.115-142, 2007.

M. Junge, C. L. Merdy, and Q. Xu, H ?-functional calculus and square functions on noncommutative L p-spaces, p.138, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00477043

M. Junge and Q. Xu, Non-commutative Burkholder/Rosenthal Inequalities, Ann. Prob, vol.31, issue.2, pp.948-995, 2003.

M. Junge and Q. Xu, Noncommutative Burkholder/Rosenthal inequalities. II. Applications. Israel J. Math, vol.167, pp.227-282, 2008.

M. Junge and Q. Xu, Noncommutative maximal ergodic theorems, J. Amer. Math. Soc, vol.20, pp.385-439, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00477047

M. Junge and T. Mei, Noncommutative Riesz transforms-a probabilistic approach, Amer. J. Math, vol.132, pp.611-681, 2010.

M. Junge and T. Mei, BMO spaces associated with semigroups of operators, Math. Ann, vol.352, pp.691-743, 2012.

M. Junge, T. Mei, and J. Parcet, Smooth Fourier multipliers on group von Neumann algebras, GAFA, vol.24, pp.1913-1980, 2014.

J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math, vol.18, pp.269-305, 1965.

C. Lance, Hilbert C *-modules. A toolkit for operator algebraists, London Mathematical Society Lecture Note Series, vol.210, 1995.

C. Lévy, C. N. Jiménez, and S. Paycha, The canonical trace and the noncommutative residue on the noncommutative torus, Trans. Amer. Math. Soc, vol.368, issue.2, pp.1051-1095, 2016.

F. Lust-piquard and G. Pisier, Noncommutative Khintchine and Paley Inequalities, Ark. Mat, vol.29, pp.241-260, 1991.

T. Mei, BMO is the intersection of two translates of dyadic BMO, C. R. Math. Acad. Sci. Paris, vol.336, issue.12, pp.1003-1006, 2003.

T. Mei, Operator-valued Hardy Spaces, Mem. Amer. Math. Soc, vol.188, issue.881, p.64, 2007.

T. Mei, Tent spaces associated with semigroups of operators, J. Funct. Anal, vol.255, issue.12, pp.3356-3406, 2008.

Y. Meyer, Régularité des solutions des équations aux dérivées partielles non linéaires (d'après, J.-M. Bony). Bourbaki Seminar, vol.80, pp.293-302, 1979.

Y. Meyer, Remarques sur un théorème de J.-M. Bony, Proceedings of the Seminar on Harmonic Analysis, 1980.

M. Musat, Interpolation between non-commutative BMO and non-commutative L pspaces, J. Funct. Anal, vol.202, issue.1, pp.195-225, 2003.

. V. Yu and . Netrusov, Embedding theorems for Lizorkin-Triebel spaces, Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), vol.47, issue.6, pp.2896-2903, 1987.

S. Neuwirth and E. Ricard, Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group, Canad. J. Math, vol.63, issue.5, pp.1161-1187, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00451399

J. Parcet, Pseudo-localization of singular integrals and noncommutative CalderónZygmund theory, J. Funct. Anal, vol.256, issue.2, pp.509-593, 2009.

J. Parcet and N. Randrianantoanina, Gundy's decomposition for non-commutative martingales and applications, Proc. London Math. Soc, vol.93, pp.227-252, 2006.

G. Pisier, Martingales in Banach spaces, Cambridge Studies in Advanced Mathematics, vol.155, 2016.

G. Pisier, Noncommutative vector valued L p spaces and completely p-summing maps, Astérisque, vol.247, p.131, 1998.

G. Pisier and Q. Xu, Non-commutative Martingale Inequalities, Comm. Math. Phys, vol.189, pp.667-698, 1997.

G. Pisier and Q. Xu, Noncommutative L p-spaces. Handbook of the geometry of Banach spaces, vol.2, pp.1459-1517, 2003.

N. Randrianantoanina, Noncommutative martingale transforms, J. Funct. Anal, vol.194, pp.181-212, 2002.

N. Randrianantoanina, Conditional square functions for noncommutative martingales, Ann. Prob, vol.35, pp.1039-1070, 2007.

N. Randrianantoanina, L. Wu, and Q. Xu, Noncommutative Davis type decompositions and applications

T. Runst, Pseudodifferential operators of the "exotic" class L 0 1,1 in spaces of Besov and Triebel-Lizorkin type, Ann. Global Anal. Geom, vol.3, issue.1, pp.13-28, 1985.

M. Ruzhansky and V. Turunen, Pseudo-differential operators and symmetries. Background analysis and advanced topics. Pseudo-Differential Operators. Theory and Applications, 2, 2010.

E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, issue.30, 1970.

E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol.43, 1993.

E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, issue.32, 1971.

M. Taylor, Pseudodifferential operator, 1981.

R. H. Torres, Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc, vol.90, issue.442, p.172, 1991.

R. H. Torres, Continuity properties of pseudodifferential operators of type 1,1. Comm. Partial Differential Equations, vol.15, pp.1313-1328, 1990.

F. Trèves, Topological vector spaces, distributions and kernels, 1967.

H. Triebel, Theory of function spaces, Modern Birkhäuser Classics. Birkhäuser/ Springer Basel AG, 2010.

H. Triebel, Theory of function spaces, II. Monographs in Mathematics, vol.84, 1992.

T. Wolff, Harmonic analysis (Minneapolis, Minn, Lecture Notes in Math, vol.908, pp.199-204, 1981.

R. Xia, X. Xiong, and Q. Xu, Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori, Adv. Math, vol.291, pp.183-227, 2016.

X. Xiong, Q. Xu, and Z. Yin, Function spaces on quantum tori, C. R. Math. Acad. Sci. Paris, vol.353, issue.8, pp.729-734, 2015.

X. Xiong, Q. Xu, Z. Yin, and . Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori, Mem. Amer. Math. Soc

Q. Xu, Noncommutative L p-spaces and martingale inequalities. Book manuscript, 2007.