Weak type inequality for logarithmic means of Walsh-Kaczmarz-Fourier series

Ushangi Goginava, Károly Nagy

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The main aim of this paper is to prove that the Nörlund logarithmic means tnκ f of one-dimensional Walsh-Kaczmarz-Fourier series is weak type (1,1), and this fact implies that tnκf converges in measure on I for every function f ∈ L(I) and tn,mκ f converges in measure on I2 for every function f ∈ Lln+ L(I2): Moreover, the maximal Orlich space such that Nörlund logarithmic means of two-dimensional Walsh-Kaczmarz-Fourier series for the functions from this space converge in two-dimensional measure is found.

Original languageEnglish
Pages (from-to)445-462
Number of pages18
JournalReal Analysis Exchange
Issue number2
Publication statusPublished - 2010
Externally publishedYes


  • Convergence in measure
  • Double Walsh-Kaczmarz-Fourier series
  • Orlicz space

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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