On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

György Gát, Ushangi Goginava, Károly Nagy

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H pq into Lorentz space L pq for every p > 2/3 and 0 < q. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ n ( f, x 1, x 2) → ( x 1, x 2) a.e. as n → ∞.

Original languageEnglish
Pages (from-to)399-421
Number of pages23
JournalStudia Scientiarum Mathematicarum Hungarica
Volume46
Issue number3
DOIs
Publication statusPublished - Sept 1 2009
Externally publishedYes

Keywords

  • Marcinkiewicz-Fejér means
  • Maximal operator
  • Primary 42C10
  • Walsh-Kaczmarz system

ASJC Scopus subject areas

  • General Mathematics

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