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Almost everywhere convergence of Vilenkin-Fourier series of $ H\sp 1$ functions


Author: Wo-Sang Young
Journal: Proc. Amer. Math. Soc. 108 (1990), 433-441
MSC: Primary 42C10
DOI: https://doi.org/10.1090/S0002-9939-1990-0998742-6
MathSciNet review: 998742
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Abstract: In [5] Ladhawala and Pankratz proved that if $ f$ is in dyadic $ {H^1}$, then any lacunary sequence of partial sums of the Walsh-Fourier series of $ f$ converges a.e. We generalize their theorem to Vilenkin-Fourier series. In obtaining this result, we prove a vector-valued inequality for the partial sums of Vilenkin-Fourier series.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0998742-6
Article copyright: © Copyright 1990 American Mathematical Society

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