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 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/S0002-9947-97-01789-3

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