The two-parameter dyadic derivative and dyadic Hardy spaces

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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 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
Volume26
Issue number2
Publication statusPublished - 2000

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Hardy Space
Two Parameters
Derivatives
Derivative
Lorentz Spaces
Maximal Function
Maximal Operator
Differentiable

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)

Cite this

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

In: Analysis Mathematica, Vol. 26, No. 2, 2000, p. 143-160.

Research output: Contribution to journalArticle

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