On The maximal operators of Vilenkin-Fejér means on Hardy spaces

Abstract

The main aim of this paper is to prove that when $0<p<1/2$ the maximal operator $\overset{\sim }{σ}_{p}^{\ast }f:=\underset{n\in \mathbb{N}}{% \sup }\frac{\left\vert σ_{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded from the martingale Hardy space $H_p$ to the space $L_p,$ where ${\sigma }_n$ is $n$-th Fejér mean with respect to bounded Vilenkin system.

arXiv commentVilenkin system, Fejér means, martingale Hardy space. arXiv admin note: substantial text overlap with arXiv:1410.6416, arXiv:1410.7075