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On the maximal operators of Vilenkin-Fejér means on Hardy spaces. (English) Zbl 1263.42008

The author proves that, when \(0<p<1/2\), the maximal operator \[ \widetilde{\sigma }_{p}^{\ast }f:=\sup\limits_{n}\frac{\left| \sigma _{n}f\right| }{\left( n+1\right) ^{1/p-2}} \] is bounded from the martingale Hardy space \(H_{p}\) to the space \(L_{p}\), where \(\sigma _{n}\) is \(n\)th Fejer-mean with respect to bounded Vilenkin system.

MSC:

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