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arXiv · 1809.06091

Noncommutative Khintchine inequalities in interpolation spaces of $L_p$-spaces

Léonard Cadilhac
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Abstract

We prove noncommutative Khintchine inequalities for all interpolation spaces between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new deterministic equivalent for the $RC$-norm in all interpolation spaces between $L_p$-spaces which unifies the cases $p > 2$ and $p < 2$. It produces a new proof of Khintchine inequalities for $p<1$ for free variables. To complete the picture, we exhibit counter-examples which show that neither of the usual closed formulas for Khintchine inequalities can work in $L_{2,\infty}$. We also give an application to martingale inequalities.

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BibTeXRIS

Léonard Cadilhac. 2018-09-17. Noncommutative Khintchine inequalities in interpolation spaces of $L_p$-spaces. https://doi.org/10.1016/j.aim.2019.06.002

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