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

 

Almost everywhere convergence
of lacunary partial sums
of Vilenkin-Fourier series


Author: Wo-Sang Young
Journal: Proc. Amer. Math. Soc. 124 (1996), 3789-3795
MSC (1991): Primary 42C10; Secondary 42B25, 43A75
MathSciNet review: 1346995
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Abstract: We prove that if $f\in L^{p},\;p>1$, and $\{n_{k}\}$ is any lacunary sequence of positive integers, then the sequence of $n_{k}$th partial sums of Vilenkin-Fourier series of $f$ converges almost everywhere to $f$.


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Additional Information

Wo-Sang Young
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03566-6
PII: S 0002-9939(96)03566-6
Received by editor(s): March 8, 1995
Received by editor(s) in revised form: June 15, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society