Almost everywhere convergence of Vilenkin-Fourier series of $H^ 1$ functions
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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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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