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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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Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
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by T. Figiel, P. Hitczenko, W. B. Johnson, G. Schechtman and J. Zinn PDF
Trans. Amer. Math. Soc. 349 (1997), 997-1027 Request permission


The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the $p$ moment of a sum of independent symmetric random variables to that of the $p$ and $2$ moments of the individual variables, are computed in the range $2<p\le 4$. This complements the work of Utev who has done the same for $p>4$. The qualitative nature of the extreme cases turns out to be different for $p<4$ than for $p>4$. The method developed yields results in some more general and other related moment inequalities.
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Additional Information
  • T. Figiel
  • Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Abrahama 18, 81–825 Sopot, Poland
  • Email:
  • P. Hitczenko
  • Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695–8205
  • Email:
  • W. B. Johnson
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 95220
  • Email:
  • G. Schechtman
  • Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel
  • MR Author ID: 155695
  • Email:
  • J. Zinn
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email:
  • Received by editor(s): December 22, 1994
  • Additional Notes: The first, second and fourth authors were participants in the NSF Workshop in Linear Analysis & Probability, Texas A&M University
    Professors Hitczenko, Johnson, and Zinn were supported in part by NSF grants
    Johnson, Schechtman and Zinn were supported in part by US–Israel Binational Science Foundation
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 997-1027
  • MSC (1991): Primary 60E15, 60G50; Secondary 26D07, 46E30
  • DOI:
  • MathSciNet review: 1390980