A sharp boundedness result concerning some maximal operators of Vilenkin-Fejér means

Abstract

In this paper we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fejér means in this subspace is bounded from the Hardy space $H_p$ to the space $L_p$ for all $0<p\le 1/2.$ Moreover, we prove that the result is in a sense sharp.