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), 9971027
MSC (1991):
Primary 60E15, 60G50; Secondary 26D07, 46E30
MathSciNet review:
1390980
Fulltext PDF Free Access
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References 
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Additional Information
Abstract: The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the moment of a sum of independent symmetric random variables to that of the and moments of the individual variables, are computed in the range . This complements the work of Utev who has done the same for . The qualitative nature of the extreme cases turns out to be different for than for . 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/S0002994797017893
PII:
S 00029947(97)017893
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
