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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A probabilistic version of Rosenthal's inequality


Authors: S. V. Astashkin and K. E. Tikhomirov
Journal: Proc. Amer. Math. Soc. 141 (2013), 3539-3547
MSC (2010): Primary 46E30, 46B09, 46B45
Published electronically: June 25, 2013
MathSciNet review: 3080175
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Abstract: We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.


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Additional Information

S. V. Astashkin
Affiliation: Department of Mathematics and Mechanics, Samara State University, 1 Akademik Pavlov str., 443011 Samara, Russia
Email: astash@samsu.ru

K. E. Tikhomirov
Affiliation: Department of Mathematics and Mechanics, Samara State University, 1 Akademik Pavlov str., 443011 Samara, Russia
Address at time of publication: Department of Mathematical and Statistical Sciences, 632 Central Academic Building, University of Alberta, Edmonton, AB, T6G 2G1 Canada
Email: ktikhomirov@yandex.ru, ktikhomi@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11713-2
PII: S 0002-9939(2013)11713-2
Keywords: Independent random variables, Rosenthal's inequality, rearrangement invariant space, quasi-normed symmetric sequence space
Received by editor(s): May 8, 2011
Received by editor(s) in revised form: December 28, 2011
Published electronically: June 25, 2013
Additional Notes: This research was partially supported by RFBR grant no. 10-01-00077
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.