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arXiv · 1501.00965

The optimal constants of the mixed $\left( \ell_{1},\ell _{2}\right) $-Littlewood inequality

Daniel Pellegrino
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Abstract

In this note, among other results, we find the optimal constants of the generalized Bohnenblust--Hille inequality for $m$-linear forms over $\mathbb{R}$ and with multiple exponents $\left( 1,2,...,2\right) $, sometimes called mixed $\left( \ell _{1},\ell _{2}\right) $-Littlewood inequality. We show that these optimal constants are precisely $\left( \sqrt{2}\right) ^{m-1}$ and this is somewhat surprising since a series of recent papers have shown that similar constants have a sublinear growth. This result answers a question raised by Albuquerque \textit{et al.} in a paper published in 2014 in the \textit{Journal of Functional Analysis}.

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Daniel Pellegrino. 2015-01-05. The optimal constants of the mixed $\left( \ell_{1},\ell _{2}\right) $-Littlewood inequality. https://arxiv.org/abs/1501.00965

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