A note on Carleson-hunt type theorems for Vilenkin-Fourier series (Q6547678)

In the present paper, an analogy of the famous Carlesson-Hunt theorem concerning bounded Vilenkin systems is investigated. Namely, the authors state that for every \(f\in L_p(G_m)\), \(p>1\), the sequence of partial sums \(S_nf\) of \(f\) with respect to a bounded Vilenkin system converges a. e. to \(f\).\N\NAlso, an analogy of the well-known Kolmogoroff's theorem about a.e. divergent trigonometric Fourier series for the bounded Vilenkin systems is investigated. Namely, the authors state that for any such system, there exists a function \(g\in L_1(G_m)\), such that the sequence of Fourier partial sums \(S_ng\) of \(g\) with respect to this system diverges a. e..\N\NFor the entire collection see [Zbl 1537.35003].