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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 Tauberian theorem for Vilenkin series


Author: W. R. Wade
Journal: Proc. Amer. Math. Soc. 131 (2003), 2877-2881
MSC (2000): Primary 42C10, 43A75
Published electronically: February 28, 2003
MathSciNet review: 1974345
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Abstract: There are a number of papers in the literature which contain Cesàro analogues of results already known for martingale sums of Vilenkin-Fourier series. We show that for Vilenkin systems of bounded type, these are not merely analogues but actually generalizations. Indeed, we prove that convergence of the Cesàro means of a Vilenkin series $S$ implies convergence of martingale partial sums of $S$ itself.


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Additional Information

W. R. Wade
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07044-8
PII: S 0002-9939(03)07044-8
Received by editor(s): April 10, 2002
Published electronically: February 28, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society