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On the maximal operators of Vilenkin-Fejér means. (English) Zbl 1278.42037

In the paper interesting results are obtained. The behaviour of Fejér means of bounded Vilenkin-Fourier series is studied. In particular, it is proved that the maximal operator \(\widetilde{\sigma}^* f:= \sup {|\sigma_n f|\over \log^2 (n+1)}\) is bounded from the Hardy space \(H_{1/2}\) to the space \(L_{1/2}\) where \(\sigma_n f\) are Fejér means of bounded Vilenkin-Fourier series.

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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