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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lacunary series and exponential moments

Authors: J. Kuelbs and W. A. Woyczyński
Journal: Proc. Amer. Math. Soc. 68 (1978), 281-291
MSC: Primary 42A44; Secondary 60F15
MathSciNet review: 0461021
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Abstract: In the present paper we prove the boundedness of second exponential moments for the suprema of norms of partial sums of random series in Banach spaces, Sidon lacunary series on a compact Abelian group with coefficients in a Banach space, and for random lacunary series with similar coefficients. Exponential moments related to the law of iterated logarithm for lacunary series are also proved to be finite. Our results, even in case of standard trigonometric series with real coefficients, strengthen the classical theorem of Salem and Zygmund.

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Keywords: Lacunary series, exponential moments, law of the iterated logarithm, Sidon sets, Banach space valued random variables
Article copyright: © Copyright 1978 American Mathematical Society