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References
Arazy, J., Some remarks on interpolation theorems and the boundedness of the triangular projection in unitary matrix spaces,Integral Equations Operator Theory,1 (1978), 453–495.
Berkson, E., Gillespie, T. A. andMuhly, P. S., Abstract spectral decompositions guaranteed by the Hilbert transform,Proc. London Math. Soc. 53 (1986), 489–517.
Blasco, O. andPelczynski, A., Theorems of Hardy and Paley for vector valued analytic) functions and related classes of Banach spaces,Trans. Amer. Math. Soc. 323 (1991) 335–367.
Bourgain, J., Some remarks on Banach spaces in which martingale differences are unconditional,Ark. Mat. 21 (1983), 163–168.
Bourgain, J., Vector valued singular integrals and theH 1-BMO duality, in:Probability theory and harmonic analysis (Chao-Woyczynski ed.), pp. 1–19. Dekker, New York, 1986.
Burkholder, D., A geometric condition that implies the existence of certain singular integrals of Banach space valued functions, in:Conference on harmonic analysis in honor of Antoni Zygmund I–II (Chicago, Ill., 1981), pp. 270–286. Wadsworth, Belmont, Calif., 1983.
Cotlar, M., A unified theory of Hilbert transforms and ergodic theory,Rev. Mat. Cuyana 1 (1955), 105–167.
Duren, P. L.,Theory of H P-spaces. Academic Press, New York, 1970.
Haagerup, U., Solution of the similarity problem for cyclic representations ofC *-algebras,Ann. Math. 118 (1983), 215–240.
Haagerup, U. andG. Pisier, Factorization of analytic functions with values in non commutativeL 1 spaces and applications,Can. J. Math. 41 (1989), 882–906.
Kahane, J.-P.,Some random series of functions (Cambridge Studies in Advanced Mathematics 5.), 2nd ed., Cambridge University Press, Cambridge, 1985.
Ledoux M. andTalagrand, M.,Isoperimetry and processes in probability in Banach spaces, Springer Verlag, Berlin-New York, 1991.
Lindenstrauss, J. andTzaffriri, L.,Classical Banach spaces, Vol. II. Springer-Verlag, Berlin-New York, 1979.
Lust-Piquard, F., Inégalités de Khintchine dansC p (1<p<∞),C. R. Acad. Sc. Paris 303 (1986), 289–292.
Lust-Piquard, F.,Inequalities in 2-convex Schatten spaces C E and a Grothendieck factorization theorem. (To appear.)
McConnell, T., On Fourier multiplier transformations of Banach valued functions,Trans. Amer. Math. Soc. 285 (1984), 739–757.
Marcus, M. andPisier, G.,Random Fourier series, with applications (Ann. Math. Studies 101.), Princeton University Press, Princeton, 1981.
Maurey, B., Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espacesL P,Astérisque 11 (1974).
Nelson, E., Notes on non commutative integration,J. Funct. Anal.,15 (1974), 104–117.
Paley, R. E. A. C., On the lacunary coefficients of a power series,Ann. Math. 34 (1933), 615–616.
Pisier, G., Grothendieck's theorem for non commutativeC * algebras with an appendix on Grothendieck's constants,J. Funct. Anal. 29 (1978), 397–415.
Pisier, G., Les inégalités de Khintchine-Kahane, d'après C. Borell, in:Séminaire sur la géométrie des espaces de Banach (1977–78). Exposé no 7, 14 pp. École Polytechnique, Palaiseau (1978).
Pisier, G.,Factorization of linear operators and geometry of Banach spaces. (Regional Conference Series in Mathematics 60.) American Mathematical Society, Providence, R. I., 1986.
Pisier, G., Probabilistic methods in the Geometry of Banach spaces, in:Probability and analysis (Varenna, 1985), pp. 167–241, Lecture Notes in Math. 1206. Springer-Verlag, Berlin-New York, 1986.
Pisier, G., Factorization of operator valued analytic functions,Adv. in Math. (To appear.)
Rubio de Francia, J. L., Martingale and integral transforms of Banach space valued functions, in:Probability and Banach spaces (Zaragoza, 1985), pp. 195–222, Lecture Notes Math. 1221. Springer-Verlag, Berlin-New York, 1986.
Sarason, D., Generalized interpolation inH ∞,Trans. Amer. Math. Soc. 127 (1967), 179–203.
Simon, B.,Trace ideals and their applications. (London Math. Soc. Lecture Notes Series 35.) Cambridge University Press, Cambridge, 1979.
Tomczak-Jaegermann, N., The moduli of smoothness and convexity of trace classS p ,Studia Math. 50 (1974), 163–182.
Tomczak-Jaegermann, N., Uniform convexity of unitary ideals,Israel J. Math. 48 (1984), 249–254.
Xu, Q., Applications du théorème de factorisation pour des fonctions à valeurs opérateurs,Studia Math. 95 (1990), 273–292.
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Lust-Piquard, F., Pisier, G. Non commutative Khintchine and Paley inequalities. Ark. Mat. 29, 241–260 (1991). https://doi.org/10.1007/BF02384340
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DOI: https://doi.org/10.1007/BF02384340