Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces

We improve and complement a result by Móricz and Siddiqi [20].In particular, we prove that their estimate of the Nörlund means with respect tothe Vilenkin system holds also without their additional condition. Moreover, weprove a similar approximation result in Lebesgue spaces for any \(1\leq p<\infty\) $1\le p<\infty$ .