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

Young, Wo-Sang

doi:10.1090/S0002-9939-96-03566-6

Almost everywhere convergence of lacunary partial sums of Vilenkin-Fourier series
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by Wo-Sang Young

Proc. Amer. Math. Soc. 124 (1996), 3789-3795

DOI: https://doi.org/10.1090/S0002-9939-96-03566-6

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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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