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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extremal properties of Rademacher functions
with applications to the Khintchine
and Rosenthal inequalities


Authors: T. Figiel, P. Hitczenko, W. B. Johnson, G. Schechtman and J. Zinn
Journal: Trans. Amer. Math. Soc. 349 (1997), 997-1027
MSC (1991): Primary 60E15, 60G50; Secondary 26D07, 46E30
MathSciNet review: 1390980
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Abstract | References | Similar Articles | Additional Information

Abstract: 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: T.Figiel@IMPAN.Gda.pl

P. Hitczenko
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695–8205
Email: pawel@math.ncsu.edu

W. B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

G. Schechtman
Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel
Email: mtschech@weizmann.weizmann.ac.il

J. Zinn
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: jzinn@plevy.math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01789-3
PII: S 0002-9947(97)01789-3
Keywords: Khintchine inequality, Rosenthal inequality, Orlicz function, extremal problem, Rademacher functions
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
Article copyright: © Copyright 1997 American Mathematical Society