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

Author(s): T. Figiel; P. Hitczenko; W. B. Johnson; G. Schechtman; J. Zinn
Journal: Trans. Amer. Math. Soc. 349 (1997), 997-1027.
MSC (1991): Primary 60E15, 60G50; Secondary 26D07, 46E30
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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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