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 countcr-example we prove that the maximal operator is not bounded from the Hardy spacc Hq to the Hardy space Hq for 0 ≤ q ≤1 and is bounded from p∑a, Da to La for some a.
In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.
