On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces

Abstract

In this paper we characterize subsequences of Fejér 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.

arXiv admin note: substantial text overlap with arXiv:1410.7978, arXiv:1504.05779, arXiv:1504.05974