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 $0<p\leq 1/2.$ Moreover, we prove that the result is in a sense sharp. 
L. E. Persson and G. Tephnadze
math.CA math.FA