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1981 Blahota, I., Gát, G. and Goginava, U. , maximal operators of Fejér means of double Vilenkin-Fourier series, Colloq. Math. , 107

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Abstract  

The aim of this paper is to prove that for an arbitrary set of measure zero there exists a bounded function for which the Fejér means of the Walsh-Fourier series of the function diverge.

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Blahota, I. and Goginava, U. , The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series, Studia Sci. Math. Hungar. , 45 (2008), 321–331. MR 2657359

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Blahota, I. and Gát, G. , Pointwise convergence of double Vilenkin-Fejér means, Studia Sci. Math. Hung. , 36 (2000), no. 1–2, 49–63. MR 2001h :42041

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convergence of double Vilenkin-Fejér means, Studia Scientiarum Mathematicarum Hungarica 36 (2000), 49–63. MR 2001h :42041 Gát G. Pointwise convergence of double Vilenkin-Fejér

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. 14 61 70 GAT, G., Pointwise convergence of Fejér means on compact totally disconnected groups, Acta Sci. Math. (Szeged) 60 (1995), 311-319. MR 96

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The main aim of this paper is to prove that the maximal operator σ 0 k*:= supnσ n,n k∣ of the Fej�r 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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convergence of double Vilenkin-Fejér means, Studia Scientiarum Mathematicarum Hungarica 36 (2000), 49–63. MR 2001h :42041 Gát G. Pointwise convergence of double Vilenkin-Fejér

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Abstract

The aim of this paper is to prove the a.e. convergence of sequences of the Fejér means of the Walsh–Fourier series of bivariate integrable functions. That is, let such that a j(n+1)≧δsupkn a j(n) (j=1,2, n∊ℕ) for some δ>0 and a 1(+∞)=a 2(+∞)=+∞. Then for each integrable function fL 1(I 2) we have the a.e. relation . It will be a straightforward and easy consequence of this result the cone restricted a.e. convergence of the two-dimensional Walsh–Fejér means of integrable functions which was proved earlier by the author and Weisz [3,8].

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Abstract  

The main aim of this paper is to prove that there exists a martingale fH 1 2/▭ such that the restricted maximal operators of Fejér means of twodimensional Walsh-Fourier series and conjugate Walsh-Fourier series does not belong to the space weak-L 1/2.

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