It is shown that the maximal operator of the two-parameter dyadic derivative of the dyadic integral is bounded from the two-parameter dyadic Hardy-Lorentz space Hp,qto Lp,q (1/2 < p < ∞, 0 < q ≤ ∞) and is of weak type (H1#, L1) where the Hardy space H1# is defined by the hybrid maximal function. As a consequence, we obtain that the dyadic integral of a two-dimensional function f ∈ H1# ⊃ L log L is dyadically differentiable and its derivative is f a.e.
|Number of pages||18|
|Publication status||Published - Dec 1 2000|
ASJC Scopus subject areas