On The maximal operators of Vilenkin-Fejér means

Abstract

The main aim of this paper is to prove that the maximal operator $\overset{% \sim }{σ}^{*}f:=\underset{n\in P}{\sup }\frac{\left| σ_{n}f\right| }{\log ^{2}\left( n+1\right) }$ is bounded from the Hardy space $H_{1/2}$ to the space $L_{1/2}$, where ${\sigma }_{n}f$ is Fejér means of bounded Vilenkin-Fourier series.

arXiv commentVilenkin system, Fejér means, martingale Hardy space. arXiv admin note: text overlap with arXiv:1410.6101