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In this paper, we find a necessary and sufficient condition for the modulus of continuity for which subsequences of Fejér means with respect to Vilenkin systems are bounded from the Hardy spaceHp{H_{p}}to the Lebesgue spaceLp{L_{p}}for all0&lt;p&lt;12{0&lt;p&lt;\frac{1}{2}}.

Modulus of continuity and convergence of subsequences of Vilenkin–Fejér means in martingale Hardy spaces