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Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars

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Diniz, D. and Muñoz-Fernández, Gustavo A. and Pellegrino, D. and Seoane-Sepúlveda, Juan B. (2014) Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars. Proceedings of the American Mathematical Society, 142 (2). pp. 575-580. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2014-142-02/S0002-9939-2013-11791-0/S0002-9939-2013-11791-0.pdf


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Abstract

The Bohnenblust-Hille inequality was obtained in 1931 and ( in the case of real scalars) asserts that for every positive integer m there is a constant Cm so that

((N)Sigma(i1 , . . . , im=1)vertical bar T(e(i1) (,...,) e(im))vertical bar(2m/m+1))(m+1/2) <= C-m parallel to T parallel to

for all positive integers N and every m-linear mapping T : l(infinity)(N) x...x l(infinity)(N) -> R. Since then, several authors have obtained upper estimates for the values of C-m. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for C-m.


Item Type:Article
Uncontrolled Keywords:Absolutely summing operators; Bohnenblust-Hille Theorem; Bohnenblust-Hille inequality
Subjects:Sciences > Mathematics > Algebra
ID Code:24705
Deposited On:17 Mar 2014 12:33
Last Modified:28 Nov 2016 08:13

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