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Random vectors satisfying Khinchine–Kahane type inequalities for linear and quadratic forms
Author(s) -
Bastero Jesús,
Romance Miguel
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310287
Subject(s) - mathematics , affine transformation , quadratic equation , inequality , combinatorics , extension (predicate logic) , type (biology) , ball (mathematics) , unit sphere , pure mathematics , mathematical analysis , geometry , ecology , computer science , biology , programming language
We study the behaviour of moments of order p (1 < p < ∞) of affine and quadratic forms with respect to non log‐concave measures and we obtain an extension of Khinchine–Kahane inequality for new families of random vectors by using Pisier's inequalities for martingales. As a consequence, we get some estimates for the moments of affine and quadratic forms with respect to a tail volume of the unit ball of l n q (0 < q < 1). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)