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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$q$-Chaos
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by Marius Junge and Hun Hee Lee PDF
Trans. Amer. Math. Soc. 363 (2011), 5223-5249 Request permission

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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Additional Information
  • Marius Junge
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
  • MR Author ID: 292431
  • Email: junge@math.uiuc.edu
  • Hun Hee Lee
  • Affiliation: Department of Mathematics, Chungbuk National University, 410 Sungbong-Ro, Heungduk-Gu, Cheongju 361-763, Korea
  • MR Author ID: 734722
  • Email: hhlee@chungbuk.ac.kr
  • Received by editor(s): January 21, 2008
  • Received by editor(s) in revised form: June 22, 2009, and July 11, 2009
  • Published electronically: May 18, 2011
  • Additional Notes: The first author was partially supported by NSF DMS - 0901457
    The second author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0015222)
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 5223-5249
  • MSC (2010): Primary 47L25; Secondary 46B07
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05165-2
  • MathSciNet review: 2813414