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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 spaceH  p{H_{p}}    to the Lebesgue spaceL  p{L_{p}}    for all0  &lt;  p  ≤  1{0&lt;p\leq 1}   . We also prove that the result is sharp in a particular sense.

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