$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative
Tom 120 / 1996
Studia Mathematica 120 (1996), 271-288
DOI: 10.4064/sm-120-3-271-288
Streszczenie
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 $f ∈ L_1$ is dyadically differentiable and its derivative is f a.e.
