Two-dimensional maximal operator of dyadic derivative on vilenkin martingale spaces

In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. 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 and is bounded from pΣα, Dα to Lα for some α.