The two-parameter dyadic derivative and dyadic Hardy spaces

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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.

Original languageEnglish
Pages (from-to)143-160
Number of pages18
JournalAnalysis Mathematica
Issue number2
Publication statusPublished - Dec 1 2000

ASJC Scopus subject areas

  • Mathematics(all)

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