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

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Abstract

The main aim of this paper is to prove that the maximal operator σ k*0 := sup n ∣σ k n,n ∣ of the Fejér means of double Fourier series with respect to the Kaczmarz system is not bounded from the Hardy space H 1/2 to the space weak-L 1/2.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Tbilisi State University, Chavchavadze str. 1, Tbilisi, 0128, Georgia

    Ushangi Goginava

  2. Institute of Mathematics and Computer Science, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400, Hungary

    Károly Nagy

Authors
  1. Ushangi Goginava
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  2. Károly Nagy
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Corresponding author

Correspondence to Ushangi Goginava.

Additional information

Communicated by László Hatvani

This paper was written during the visit of the first author at the College of Nyíregyháza in Hungary.

Supported by the Hungarian NFSR (OTKA), grant no. M 36511/2001, T 048780.

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Goginava, U., Nagy, K. On the Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. Period Math Hung 55, 11–18 (2007). https://doi.org/10.1007/s10998-007-3011-5

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  • DOI: https://doi.org/10.1007/s10998-007-3011-5

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