Abstract
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.
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