### 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 |
---|---|

Pages (from-to) | 143-160 |

Number of pages | 18 |

Journal | Analysis Mathematica |

Volume | 26 |

Issue number | 2 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Mathematics(all)

### Cite this

*Analysis Mathematica*,

*26*(2), 143-160.

**The two-parameter dyadic derivative and dyadic Hardy spaces.** / Weisz, F.

Research output: Contribution to journal › Article

*Analysis Mathematica*, vol. 26, no. 2, pp. 143-160.

}

TY - JOUR

T1 - The two-parameter dyadic derivative and dyadic Hardy spaces

AU - Weisz, F.

PY - 2000

Y1 - 2000

N2 - 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 1 #, 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.

AB - 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 1 #, 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.

UR - http://www.scopus.com/inward/record.url?scp=11844285307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11844285307&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:11844285307

VL - 26

SP - 143

EP - 160

JO - Analysis Mathematica

JF - Analysis Mathematica

SN - 0133-3852

IS - 2

ER -