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arXiv · 0801.3704

$q$-Chaos

Marius Junge·Hun Hee Lee
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Abstract

We consider the $L_p$ norm estimates for homogeneous polynomials of $q$-gaussian variables ($-1\leq q\leq 1$). When $-1<q<1$ the $L_p$ estimates for $1\leq p \leq 2$ are essentially the same as the free case ($q=0$), whilst the $L_p$ estimates for $2\leq p \leq \infty$ show a strong $q$-dependence. Moreover, the extremal cases $q = \pm 1$ produce decisively different formulae.

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Marius Junge, Hun Hee Lee. 2008-01-24. $q$-Chaos. https://arxiv.org/abs/0801.3704

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