Some maximal lnequalities with respect to two-parameter dyadic derivative and cesàro summability

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Abstract

We consider two-dimensional convolution operators with general kernel functions and give a sufficient condition for the two-parameter maximal operator to be bounded from the dyadic martingale Hardy space H p to L p . Especially, the boundedness of the maximal operator of the twoparameter dyadic derivative of the dyadic integral function and the maximal operator of the two-parameter Cesàro means are verified. As a consequence we obtain that every function f ∈ L log+ L[O, 1) 2 is Cesho summable and the dyadic integral of it is dyadically differentiable.

Original languageEnglish
Pages (from-to)223-238
Number of pages16
JournalInternational Journal of Phytoremediation
Volume62
Issue number3-4
DOIs
Publication statusPublished - Oct 1996

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Keywords

  • Cesàro summability
  • Dyadic derivative
  • Interpolation
  • Martingale hardy spaces
  • Quasi-local operators
  • Rectangle atoms
  • Walsh function

ASJC Scopus subject areas

  • Environmental Chemistry
  • Pollution
  • Plant Science

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