Abstract
In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust–Hille inequality introduced in Albuquerque et al. (J Funct Anal 266:3726–3740, 2014). 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 Pellegrino (J Number Theory 160:11–18, 2016) and Pellegrino and Teixeira (Commun Contemp Math, to appear).
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The authors are indebted to the anonymous referee for his/her important contributions to the final version of this paper.
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This paper is dedicated to Julieta.
N. Caro is supported by FACEPE Grant APQ-0892-1.01/14, D. Núñez and D. M. Serrano are supported by Capes Grants 000785/2015-06 and 000786/2015-02, respectively.
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Caro, N., Núñez-Alarcón, D. & Serrano-Rodríguez, D.M. On the generalized Bohnenblust–Hille inequality for real scalars. Positivity 21, 1439–1455 (2017). https://doi.org/10.1007/s11117-017-0478-9
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DOI: https://doi.org/10.1007/s11117-017-0478-9