Maximal operator of dyadic derivative on Vilenkin Group

Abstract

In [1], the boundeness of one dimensional maximal operator of dyadic derivative is discussed. Unfortunately, the proof is uncorrect. In this paper, we consider the maximal operator of dyadic derivative on Vilenin group. With the help of counter-example we prove that the maximal operator is not bounded from the Hardy space Hq to the Hardy space Hq for 0 < q ≤ 1.