On the boundedness of subsequences of Vilenkin-Fej\'er means on the martingale Hardy spaces

In this paper we characterize subsequences of Fej'er means with respect to Vilenkin systems, which are bounded from the Hardy space $H_p$ to the Lebesgue space $L_p,$ for all $0<p<1\mathrm{/}2.$ The result is in a sense sharp.