A sharp boundedness result concerning some maximal operators of Vilenkin-Fej\'er means

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