## 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

## 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.## References

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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
- MR Author ID: 95220
- Email: johnson@math.tamu.edu
**G. Schechtman**- Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel
- MR Author ID: 155695
- 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
- 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: https://doi.org/10.1090/S0002-9947-97-01789-3
- MathSciNet review: 1390980