Campos, J.R.Jiménez Rodríguez, P.Muñoz-Fernández, Gustavo A.Pellegrino, D.Seoane-Sepúlveda, Juan B.2023-06-192023-06-192015[1] F. Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), 203–236. [2] F. Bayart, D. Pellegrino, and J. B. Seoane-Sepulveda, The Bohr radius of the n-dimensional polydisk is equivalent to p(log n)/n, arXiv:1310.2834 [math.FA]. [3] H. P. Boas, The football player and the infinite series, Notices Amer. Math. Soc. 44 (1997), no. 11, 1430–1435. [4] H. P. Boas and D. Khavinson, Bohr’s power series theorem in several variables, Proc. Amer. Math. Soc. 125 (1997),no. 10, 2975–2979. [5] H. F. Bohnenblust and E. Hille, On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), no. 3,600–622. [6] A. Defant, L. Frerick, J. Ortega-Cerda, M. Ounaıes, and K. Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), no. 1, 485–497. [7] J. Diestel, H. Jarchow, and A. Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics,vol. 43, Cambridge University Press, Cambridge, 1995. [8] D. Diniz, G. A. Muñoz-Fernandez, D. Pellegrino, and J. B. Seoane-Sepulveda, The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal, J. Funct. Anal. 263 (2012), 415–428. [9] D. Diniz, G. A. Muñoz-Fernandez, D. Pellegrino, and J. B. Seoane-Sep´ulveda, Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars, Proc. Amer. Math. Soc. 142 (2014), 575–580. [10] P. Erdos, Some remarks on polynomials, Bull. Amer. Math. Soc. 53 (1947), 1169–1176. [11] A. Montanaro, Some applications of hypercontractive inequalities in quantum information theory, J. Math. Physics 53 (2012). [12] D. Nuñez-Alarc´on, A note on the polynomial Bohnenblust-Hille inequality, J. Math. Anal. Appl. 407 (2013), no. 1,179–181. [13] D. Pellegrino and J. B. Seoane-Sepulveda, New upper bounds for the constants in the Bohnenblust-Hille inequality, J.Math. Anal. Appl. 386 (2012), no. 1, 300–307. [14] H. Queffelec, H. Bohr’s vision of ordinary Dirichlet series: old and new results, J. Anal. 3 (1995), 43–60. [15] C. Visser, A generalization of Tchebychef ’s nequality to polynomials in more than one variable, Nederl. Akad. Wetensch., Proc. 49 (1946), 455–456 = Indagationes Math. 8, 310–311 (1946).0024-379510.1016/j.laa.2014.09.040https://hdl.handle.net/20.500.14352/33772Abstract. It was recently proved by Bayart et al. that the complex polynomial Bohnenblust–Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if DR,m stands for the real Bohnenblust–Hille constant for m-homogeneous polynomials, then lim sup(m) D-R,m(1/m) = 2, a quite surprising result having in mind that the exact value of the Bohnenblust-Hille constants is still a mystery.engjournal articlehttp://arxiv.org/pdf/1209.4632v7.pdfhttp://www.sciencedirect.com/open access517.98Bohnenblust–Hille inequalityAbsolutely summing operators.Análisis funcional y teoría de operadores