𝑞-Chaos

Junge, Marius; Lee, Hun Hee

doi:10.1090/S0002-9947-2011-05165-2

$q$-Chaos
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by Marius Junge and Hun Hee Lee

Trans. Amer. Math. Soc. 363 (2011), 5223-5249

DOI: https://doi.org/10.1090/S0002-9947-2011-05165-2

Published electronically: May 18, 2011

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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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