A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces

Abstract

Abstract The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H_{p}} to the Lebesgue space L p {L_{p}} for all 0 < p ≤ 1 {0<p\leq 1} . We also prove that the result is sharp in a particular sense.