### Abstract

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 H_{p,q}to L_{p,q} (1/2 < p < ∞, 0 < q ≤ ∞) and is of weak type (H_{1}^{#}, L_{1}) where the Hardy space H_{1}^{#} is defined by the hybrid maximal function. As a consequence, we obtain that the dyadic integral of a two-dimensional function f ∈ H_{1}^{#} ⊃ L log L is dyadically differentiable and its derivative is f a.e.

Original language | English |
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Pages (from-to) | 143-160 |

Number of pages | 18 |

Journal | Analysis Mathematica |

Volume | 26 |

Issue number | 2 |

Publication status | Published - Dec 1 2000 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Weisz, F. (2000). The two-parameter dyadic derivative and dyadic Hardy spaces.

*Analysis Mathematica*,*26*(2), 143-160.