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On the generalized Bohnenblust-Hille inequality for real scalars. (English) Zbl 06816310
Summary: In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust-Hille inequality introduced in [N. Albuquerque et al., J. Funct. Anal. 266, No. 6, 3726–3740 (2014; Zbl 1319.46035)]. We apply these results to find optimal constants in the generalized Bohnenblust-Hille inequality and also to recover the optimal constants of the mixed \(\left( \ell_{1},\ell_{2}\right) \)-Littlewood inequalities recently obtained in [D. Pellegrino, J. Number Theory 160, 11–18 (2016; Zbl 1431.46024); with E. V. Teixeira, “Towards sharp Bohnenblust-Hille constants”, Commun. Contemp. Math., Article ID 750029 (2017; doi:10.1142/s0219199717500298), arXiv:1604.07595].

MSC:
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables
47H60 Multilinear and polynomial operators
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