This is an announcement for the paper "Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars" by Diogo Diniz, Gustavo Munoz-Fernandez, Daniel Pellegrino and Juan B. Seoane-Sepulveda.
Abstract: The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer $N$ and every $m$-linear mapping $T:\ell_{\infty}^{N}\times\cdots\times\ell_{\infty}^{N}\rightarrow \mathbb{R}$ one has \begin{equation*} \left( \sum\limits_{i_{1},...,i_{m}=1}^{N}\left\vert T(e_{i_{^{1}}},...,e_{i_{m}})\right\vert ^{\frac{2m}{m+1}}\right) ^{\frac{m+1}{2m}}\leq C_{m}\left\Vert T\right\Vert , \end{equation*} for some positive constant $C_{m}$. Since then, several authors 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 $C_{m}$.
Archive classification: math.FA
Submitted from: dmpellegrino@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.3253
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