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On the Bohnenblust-Hille inequality and a variant of Littlewood's 4/3 inequality

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Nuñez Alarcón, D and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B. (2013) On the Bohnenblust-Hille inequality and a variant of Littlewood's 4/3 inequality. Journal of Functional Analysis, 264 (1). pp. 326-336. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123612003886




Abstract

The search for sharp constants for inequalities of the type Littlewood's 4/3 and Bohnenblust-Hille has lately shown unexpected applications in many fields such as Analytic Number Theory, Quantum Information Theory, or in results on n-dimensional Bohr radii. Recent estimates obtained for the multilinear Bohnenblust-Hille inequality (for real scalars) have been used, as a crucial tool, by A. Montanaro in order to solve problems in Quantum XOR games. Here, among other results, we obtain new upper bounds for the Bohnenblust-Hille constants (for complex scalars). For bilinear forms, we provide optimal constants of variants of Littlewood's 4/3 inequality (for real scalars) when the exponent 4/3 is replaced by any r >= 4/3. We also prove that the optimal constants in real case are always strictly greater than those from the complex case.


Item Type:Article
Uncontrolled Keywords:Bohnenblust–Hille Theorem; Littlewood’s 4/3 inequality; Steinhaus random variables
Subjects:Sciences > Physics > Mathematical physics
ID Code:19924
Deposited On:12 Feb 2013 16:44
Last Modified:28 Nov 2016 08:20

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