### $({H}_{p},{L}_{p})$-type inequalities for the two-dimensional dyadic derivative

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 ${H}_{p,q}$ to ${L}_{p,q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $({L}_{1},{L}_{1})$. As a consequence we show that the dyadic integral of a ∞ function $f\in {L}_{1}$ is dyadically differentiable and its derivative is f a.e.