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  • 1 University of Budapest “Elte” Department of Numerical Analysis Múzeum KRT. 6-8 1088 Budapest Hungary
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It is shown that the maximal operator of the one-dimensional dyadic derivative of the dyadic integral is bounded from the dyadic Hardy-Lorentz spaceHp,q toLp,q (1/2<p<∞, 0<q≤∞) and is of weak type (L1,L1). We define the twodimensional dyadic hybrid Hardy spaceH1 and verify that the corresponding maximal operator of a two-dimensional function is of weak type (H1 ,L1). As a consequence, we obtain that the dyadic integral of a two-dimensional functionfεH1LlogL is dyadically differentiable and its derivative is a.e.f.