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On an Estimate of the Partial Sums of Vilenkin-Fourier

Published online by Cambridge University Press:  20 November 2018

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

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We show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].

Keywords

42C1043A75
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 426 - 432
Copyright
Copyright © Canadian Mathematical Society 1991

References

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