Open Access𝑞-Chaos
Author(s) -
Marius Junge,
Hun Hee Lee
Publication year - 2011
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2011-05165-2
Subject(s) - algorithm , annotation , computer science , artificial intelligence
We consider the L p L_p norm estimates for homogeneous polynomials of q q -Gaussian variables ( − 1 ≤ q ≤ 1 -1\leq q\leq 1 ). When − 1 > q > 1 -1>q>1 the L p L_p estimates for 1 ≤ p ≤ 2 1\leq p \leq 2 are essentially the same as the free case ( q = 0 q=0 ), whilst the L p L_p estimates for 2 ≤ p ≤ ∞ 2\leq p \leq \infty show a strong q q -dependence. Moreover, the extremal cases q = ± 1 q = \pm 1 produce decisively different formulae.