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Maximal operators of Fejér means of double Vilenkin–Fourier series

Volume 107 / 2007

István Blahota, György Gát, Ushangi Goginava Colloquium Mathematicum 107 (2007), 287-296 MSC: Primary 42C10. DOI: 10.4064/cm107-2-8

Abstract

The main aim of this paper is to prove that the maximal operator $\sigma _{0}^{*}:=\sup_{n}| \sigma _{n,n}| $ of the Fejér means of the double Vilenkin–Fourier series is not bounded from the Hardy space $% H_{1/2}$ to the space weak-$L_{1/2}$.

Authors

  • István BlahotaInstitute of Mathematics and
    Computer Science
    College of Nyíregyháza
    P.O. Box 166
    Nyíregyháza, H-4400 Hungary
    e-mail
  • György GátInstitute of Mathematics and
    Computer Science
    College of Nyíregyháza
    P.O. Box 166
    Nyíregyháza, H-4400 Hungary
    e-mail
  • Ushangi GoginavaDepartment of Mechanics and Mathematics
    Tbilisi State University
    Chavvadze Str. 1
    Tbilisi 0128, Georgia
    e-mail

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