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

Abstract

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 $0<p<1/2.$ The result is in a sense sharp.