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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space to (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type . As a consequence we show that the dyadic integral of a ∞ function is dyadically differentiable and its derivative is f a.e.
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