We demonstrate conditions for various types of convergence of Vilenkin-Fourier series in function spaces, suggesting significant implications for analysis.
We give sufficient conditions for a.e. convergence of Vilenkin-Fourier series on $$[0,1)$$ , pointwise one on $$(0,1)$$ and uniform convergence on [ε,1) , ε∈ (0,1) , in terms of behavior of some linear means of cited above series. Also, a condition for such means to converge a.e. on $$[0,1)$$ is proved.
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Agafonova et al. (2026) studied this question.
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